Ex 7.4 Class 12 Maths Question 9. Solution: Miscellaneous Exercise Class 11 Maths Question 13: Ex 7.2 Class 12 Maths Question 32. The integral evaluates as 1 3 r3 2 + ln jr + C: 15. Ex 7.2 Class 12 Maths Question 20. If we are lucky enough to find the function on the result side of a derivative, then (knowing that derivatives and integrals are opposites) we have an answer. Solution: Ex 7.9 Class 12 Maths Question 12. Integration Questions. $$\int _{ 0 }^{ \frac { \pi }{ 4 } }{ tanx\quad dx }$$ हल- Solution: Solution: Miscellaneous Exercise Class 11 Maths Question 41: Solution: Solution: This tutorial begins with a discussion of antiderivatives, mathematical objects that are closely related to derivatives. $$\frac { cosx }{ 1+cosx }$$ $$\int { \frac { dx }{ { sin }^{ 2 }x{ \quad cos }^{ 2 }x } = }$$ $$\frac { 1 }{ \sqrt { { (2-x) }^{ 2 }+1 } }$$ $${ sin\quad 2x-4e }^{ 3x }$$ So, in the part we are only going to integrate the first term. mathematics openly and to share their learning. Ex 7.6 Class 12 Maths Question 14. $$\sqrt { 1-{ 4x }^{ 2 } }$$ And the increase in volume can give us back the flow rate. Solution: Ex 7.5 Class 12 Maths Question 10. Advanced Math Solutions â Integral Calculator, the basics Integration is the inverse of differentiation. Ex 7.1 Class 12 Maths Question 19. Solution: Miscellaneous Exercise Class 11 Maths Question 29: Ex 7.10 Class 12 Maths Question 7: $$\frac { 3x }{ 1+{ 2x }^{ 4 } }$$ Ex 7.6 Class 12 Maths Question 15. Solution: Miscellaneous Exercise Class 11 Maths Question 16: C3 A Level Maths Integration answers Author: maths made easy Subject: a level maths Keywords: a level, maths, free, worksheets, questions, revision, resources, integration Created â¦ ∫cos2x cos4x cos6x dx = ∫(sec² x dx (c) $$\frac { 2 }{ 3 } x{ \left( 1+{ x }^{ 2 } \right) }^{ \frac { 3 }{ 2 } }+c$$ Ex 7.6 Class 12 Maths Question 6. Ex 7.4 Class 12 Maths Question 12. We have been doing Indefinite Integrals so far. x sec²x $$\int { \frac { 1 }{ cos(x-a)cos(x-b) } dx }$$ Solution: Miscellaneous Exercise Class 11 Maths Question 6: Ex 7.6 Class 12 Maths Question 11. (a) $$\frac { \pi }{ 3 }$$ Solution: Ex 7.6 Class 12 Maths Question 2. Ex 7.5 Class 12 Maths Question 17. Solution: Integration is one of the two main operations of calculus; its inverse operation, differentiation, is the other. But it is often used to find the area underneath the graph of a function like this: The integral of many functions are well known, and there are useful rules to work out the integral â¦ (d) $${ x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } -\frac { 129 }{ 8 }$$ Solution: The integral of product of two functions of x is evaluated with the help of integration by parts. Solution: Ex 7.3 Class 12 Maths Question 21. Solution: Miscellaneous Exercise Class 11 Maths Question 14: Itâs not all about answering questions on screen. These complicated indefinite integrals include the integral of a constant (the constant times x), the integral of e x (e x) and the integral of x-1 (ln[x]). Ex 7.2 Class 12 Maths Question 16. Miscellaneous Exercise Class 11 Maths Question 11: = 2∫x² dx – 3 ∫ sinx dx + 5∫√x dx, Ex 7.1 Class 11 Maths प्रश्न 18. Solution: Ex 7.6 Class 12 Maths Question 24. Solution: Ex 7.8 Class 12 Maths Question 6. Ex 7.2 Class 12 Maths Question 13. e2x Solution: Miscellaneous Exercise Class 11 Maths Question 26: (b) $$\frac { 1 }{ 3 } +{ e }^{ { x }^{ 2 } }+c$$ Solution: $$\frac { 3x-1 }{ { (x+2) }^{ 2 } }$$ Ex 7.2 Class 12 Maths Question 3. (a) -cot(e.xx)+c Ex 7.6 Class 12 Maths Question 10. Solution: हल- Solution: Application of Integrals Class 12 Maths MCQs Pdf. $$\sqrt { sin2x } cos2x$$ $$\frac { 1 }{ sinx{ cos }^{ 3 }x }$$ Solution: $$\int { { x }^{ 2 }{ e }^{ { x }^{ 3 } } } dx\quad equals$$ Instead, it approximates a function $$f$$ with constant functions on small subintervals and then computes the definite integral of these constant functions. Ex 7.3 Class 12 Maths Question 3. $$\frac { x }{ \left( { x }^{ 2 }+1 \right) \left( x-1 \right) }$$ Solution: 8) Without integrating, determine whether the integral $$\displaystyle â«^â_1\frac{1}{\sqrt{x+1}}\,dx$$ converges or diverges. Ex 7.1 Class 12 Maths Question 1. Ex 7.1 Class 12 Maths Question 4. Solution: The input (before integration) is the flow rate from the tap. $$\frac { cos\sqrt { x } }{ \sqrt { x } }$$ Ex 7.2 Class 12 Maths Question 22. Solution: Ex 7.8 Class 12 Maths Question 4. Solution: Solution: Ex 7.9 Class 12 Maths Question 2. Class 12 Maths Integrals NCERT Solutions for CBSE Board, UP Board, MP Board, Bihar, Uttarakhand board â¦ (d) $${ sin }^{ -1 }\left( \frac { 9x-8 }{ 9 } \right) +c$$ हल- Ex 7.10 Class 12 Maths Question 14: You can also check your answers! Solution: (c) $$log\left| \left( \frac { x-{ 1 }^{ 2 } }{ x-2 } \right) \right| +c$$ $$\int { \frac { { x }^{ 3 }-{ x }^{ 2 }+x-1 }{ x-1 } dx }$$ $$\int { { e }^{ x }secx(1+tanx) } dx\quad equals$$ $$\frac { 4x+1 }{ \sqrt { { 2x }^{ 2 }+x-3 } }$$ Solution: Ex 7.9 Class 12 Maths Question 10. Solution: Solution: Ex 7.9 Class 12 Maths Question 6. Solution: Integral is designed to develop the deep understanding and skills you need to excel in maths. Integrals Class 12 [â¦] (d) tan-1x+c (ax + c)² $$\int { \left( { 2x }^{ 2 }+{ e }^{ x } \right) dx }$$ cotx log sinx $${ e }^{ x }(sinx+cosx)$$ Ex 7.3 Class 12 Maths Question 9. $$\frac { x }{ \sqrt { x+4 } } ,x>0$$ Old Exam Questions with Answers 49 integration problems with answers. $$\frac { cos2x }{ { (cosx+sinx) }^{ 2 } }$$ Solution: Ex 7.2 Class 12 Maths Question 34. (a) xtan-1(x+1)+c Solution: Solution: sin 2x – 4e3x introduce an integration trick, which solves integral by flipping variableâs direction, and demonstrate the trick using 4 examples. $$\int _{ 2 }^{ 3 }{ \frac { x }{ { x }^{ 2 }+1 } } dx$$ Solution: $$\frac { 1 }{ \sqrt { { x }^{ 2 }+2x+2 } }$$ Well, we have played with y=2x enough now, so how do we integrate other functions? $$x\quad { cos }^{ -1 }x$$ 57 series problems with answers. $$\frac { { e }^{ x }(1+sinx) }{ 1+cosx }$$ Solution: sin 2x (b) $$\frac { 2 }{ 3 } { x }^{ \frac { 2 }{ 3 } }+{ \frac { 1 }{ 2 } x }^{ 2 }+c$$ Solution: Ex 7.8 Class 12 Maths Question 5. Ex 7.10 Class 12 Maths Question 18: and then finish with dx to mean the slices go in the x direction (and approach zero in width). Integration: With a flow rate of 1, the tank volume increases by x, Derivative: If the tank volume increases by x, then the flow rate is 1. $$\int _{ a }^{ b }{ x\quad dx }$$ $$\frac { 1 }{ \sqrt { 1+{ 4x }^{ 2 } } }$$ $$\frac { 3x-1 }{ (x-1)(x-2)(x-3) }$$ Choose the correct answer in the Exercises 10 to 11: Ex 7.7 Class 12 Maths Question 10. (b) tan(xex)+c tan²(2x-3) Ex 7.7 Class 12 Maths Question 7. $$\frac { x }{ (x-1)(x-2)(x-3) }$$ Solution: Ex 7.6 Class 12 Maths Question 18. Ex 7.4 Class 12 Maths Question 5. $$\frac { 1 }{ x-\sqrt { x } }$$ Ex 7.5 Class 12 Maths Question 22. If youâd like a pdf document containing the solutions the download tab above contains links to pdfâs containing the solutions for the full book, chapter and section. $$\frac { { e }^{ 2x }-1 }{ { e }^{ 2x }+1 }$$ Solution: Integration is a way of adding slices to find the whole. $$\frac { 1 }{ { 9x }^{ 2 }+6x+5 }$$ Solution: A Definite Integral has actual values to calculate between (they are put at the bottom and top of the "S"): At 1 minute the volume is increasing at 2 liters/minute (the slope of the volume is 2), At 2 minutes the volume is increasing at 4 liters/minute (the slope of the volume is 4), At 3 minutes the volume is increasing at 6 liters/minute (a slope of 6), The flow still increases the volume by the same amount. Ex 7.2 Class 12 Maths Question 18. Ex 7.5 Class 12 Maths Question 7. $$\frac { x }{ { e }^{ { x }^{ 2 } } }$$ Solution: Ex 7.4 Class 12 Maths Question 20. Ex 7.4 Class 12 Maths Question 13. Solution: Ex 7.6 Class 12 Maths Question 21. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. $${ ta }n^{ -1 }x$$ Solution: Imagine the flow starts at 0 and gradually increases (maybe a motor is slowly opening the tap). Solution: Ex 7.2 Class 12 Maths Question 30. So get to know those rules and get lots of practice. ∫(2x – 3cosx + ex)dx, प्रश्न 17. Solution: Ex 7.9 Class 12 Maths Question 19. Solution: =∫(√x-x√x)dx, Ex 7.1 Class 11 Maths प्रश्न 15. Solution: $$\frac { 3x+5 }{ { x }^{ 3 }-{ x }^{ 2 }-x+1 }$$ Solution: So Integral and Derivative are opposites. (c) $$\frac { 1 }{ 2 } { e }^{ { x }^{ 3 } }+c$$ ∫secx (sec x + tan x) dx sin 2x $$\int _{ -1 }^{ 1 }{ { (x+1 }) } dx\quad$$ Integration: With a flow rate of 2x, the tank volume increases by x2, Derivative: If the tank volume increases by x2, then the flow rate must be 2x. Solution: Miscellaneous Exercise Class 11 Maths Question 2: Integration can be used to find areas, volumes, central points and many useful things. put 5x-2=A$$\frac { d }{ dx }$$(1+2x+3x²)+B Ex 7.1 Class 12 Maths Question 17. Solution: The symbol for "Integral" is a stylish "S" Ex 7.1 Class 12 Maths Question 21. MEI is an independent charity, committed to improving maths education. $$\int { \frac { { x }^{ 3 }+{ 5x }^{ 2 }-4 }{ { x }^{ 2 } } dx }$$ Solution: I = $$\frac { 1 }{ 2 }$$ ∫sec²t dt-x+c ∫√x(3x² + 2x + 3)dx, Ex 7.1 Class 11 Maths प्रश्न 16. Solution: $$\frac { { (1+logx) }^{ 2 } }{ x }$$ The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 7 Integrals. $$\frac { x+2 }{ \sqrt { { x }^{ 2 }-1 } }$$ ∫(1-x)√x dx $${ sin }^{ -1 }\left( \frac { 2x }{ 1+{ x }^{ 2 } } \right)$$ Solution: Ex 7.3 Class 12 Maths Question 18. Ex 7.6 Class 12 Maths Question 22. Ex 7.4 Class 12 Maths Question 24. Ex 7.5 Class 12 Maths Question 11. Ex 7.5 Class 12 Maths Question 21. ∫cos 3x dx $$\int { \frac { xdx }{ (x-1)(x-2) } equals }$$ ∫(ax² + bx + c) dx = a∫x²dx + b∫xdx + c∫1 dx, Ex 7.1 Class 11 Maths प्रश्न 9. Practice! Solution: Solution: Solution: $$\frac { cosx }{ (1-sinx)(2-sinx) }$$ Solution: sin3x cos3x Indefinite Integration (Polynomial, Exponential, Quotient) How to determine antiderivatives using integration formulas? Ex 7.5 Class 12 Maths Question 19. Solution: Miscellaneous Exercise Class 11 Maths Question 5: $$\frac { 1 }{ \sqrt { (x-a)(x-b) } }$$ Solution: Solution: Integral the function in exercises 1 to 9. Solution: Miscellaneous Exercise Class 11 Maths Question 44: (d) log|(x-1)(x-2)|+c $$\frac { 1 }{ \sqrt { 7-6x-{ x }^{ 2 } } }$$ Solution: Miscellaneous Exercise Class 11 Maths Question 27: $$\frac { 1 }{ 1+cotx }$$ sin3x cos4x Ex 7.2 Class 12 Maths Question 12. (a) $$\frac { \pi }{ 6 }$$ Solution: $$\int _{ \frac { \pi }{ 6 } }^{ \frac { \pi }{ 4 } }{ cosec\quad xdx }$$ Solution: Ex 7.3 Class 12 Maths Question 20. Integrate the functions in Exercises 1 to 37: Ex 7.2 Class 12 Maths Question 1. Ex 7.1 Class 12 Maths Question 12. हल- Integration can be used to find areas, volumes, central points and many useful things. (c) tanx cotx + c Solution: Solution: Solution: Ex 7.8 Class 12 Maths Question 1. After the integral is introduced via the area problem, the integral and the antiderivative are shown to be related by an amazing theorem called â¦ Ex 7.6 Class 12 Maths Question 9. Solution: Imagine you don't know the flow rate. (c) $$\frac { \pi }{ 24 }$$ $$\frac { { sin }^{ 3 }x+{ cos }^{ 3 }x }{ { sin }^{ 2 }x{ cos }^{ 2 }x }$$ In exercises 9 - 25, determine whether the improper integrals converge or diverge. ∫sin 2x dx Solution: (c) tan(ex)+c If possible, determine the value of the integrals that converge. $$\frac { 1 }{ 1-tanx }$$ Solution: Solution: Miscellaneous Exercise Class 11 Maths Question 34: Ex 7.10 Class 12 Maths Question 9: Solution: Ex 7.9 Class 12 Maths Question 16. Ex 7.3 Class 12 Maths Question 2. Solution: Ex 7.9 Class 12 Maths Question 7. हल- Ex 7.5 Class 12 Maths Question 3. Solution: Ex 7.2 Class 12 Maths Question 9. Ex 7.2 Class 12 Maths Question 17. (x²+1)logx Ex 7.2 Class 12 Maths Question 37. Solution: Because ... ... finding an Integral is the reverse of finding a Derivative. sin²(2x+5) Solution: (d) $$\frac { 1 }{ 2 } log|x|+log({ x }^{ 2 }+1)+c$$ $$\int _{ 0 }^{ 4 }{ { (x+e }^{ 2x }) } dx\quad$$ Solution: निम्नलिखित फलनों के प्रतिअवकलज ( समाकलन) निरीक्षण विधि द्वारा ज्ञात कीजिए।, Ex 7.1 Class 11 Maths प्रश्न 1. $$\frac { 1 }{ { e }^{ x }-1 }$$ Ex 7.1 Class 12 Maths Question 20. Solution: Ex 7.5 Class 12 Maths Question 1. But it is easiest to start with finding the area under the curve of a function like this: We could calculate the function at a few points and add up slices of width Δx like this (but the answer won't be very accurate): We can make Δx a lot smaller and add up many small slices (answer is getting better): And as the slices approach zero in width, the answer approaches the true answer. $$\int { \left( { 2x }^{ 2 }-3sinx+5\sqrt { x } \right) dx }$$ $$\int { \frac { dx }{ x({ x }^{ 2 }+1) } equals }$$ (d) tanx+secx+c $$\sqrt { 4-{ x }^{ 2 } }$$ Solution: Solution: $$\frac { 2x-3 }{ ({ x }^{ 2 }-1)(2x+3) }$$ Solution: Ex 7.9 Class 12 Maths Question 21. The antiderivative $$\left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right)$$ equals Ex 7.2 Class 12 Maths Question 39. Solution: (c) $$\frac { 1 }{ 3 } { sin }^{ -1 }\left( \frac { 9x-8 }{ 8 } \right) +c$$ $$\frac { x }{ 9-4{ x }^{ 2 } }$$ Ex 7.3 Class 12 Maths Question 8. (d) $$\frac { \pi }{ 4 }$$ Solution: Solution: ∫sinx4 dx Ex 7.7 Class 12 Maths Question 2. $$\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin2x\quad dx }$$ $$\sqrt { 1+3x-{ x }^{ 2 } }$$ $$\int { secx(secx+tanx)dx }$$ $$\frac { { sec }^{ 2 }x }{ \sqrt { { tan }^{ 2 }x+4 } }$$ Solution: ∫(2x² – 3sinx + 5√x)dx sin-1 (cos x) ∫√x(3x² + 2x + 3)dx Solution: firstly the definite integral was expressed as a limit of a certain sum expressing the area of some region. Solution: Integrals Important Questions for CBSE Class 12 Maths Types of Integrals. Solution: Ex 7.9 Class 12 Maths Question 14. Ex 7.4 Class 12 Maths Question 3. Solution: Miscellaneous Exercise Class 11 Maths Question 12: $$\int _{ 0 }^{ 1 }{ \frac { 2x+3 }{ { 5x }^{ 2 }+1 } dx }$$ Ex 7.6 Class 12 Maths Question 17. They must also go through the NCERT solutions for Class 12 Maths and Class 11 Maths to have a better understanding of the various concepts. $\int{{6{x^5}\,dx}} - 18{x^2} + 7 = \require{bbox} \bbox[2pt,border:1px solid black]{{{x^6} + c - 18{x^2} + 7}}$ Solution: Ex 7.9 Class 12 Maths Question 5. = ∫sec x tan x dx $$\frac { { \left( logx \right) }^{ 2 } }{ x }$$ $$\frac { sinx }{ 1+cosx }$$ Ex 7.2 Class 12 Maths Question 27. $$\int { \frac { 2-3sinx }{ { cos }^{ 2 }x } dx }$$ (there are some questions below to get you started). You only know the volume is increasing by x2. Solution: Ex 7.9 Class 12 Maths Question 18. Solution: $$\int { { (ax }^{ 2 }+bx+c)dx }$$ Ex 7.7 Class 12 Maths Question 8. $$\int _{ 0 }^{ \pi }{ \left( { sin }^{ 2 }\frac { x }{ 2 } -{ cos }^{ 2 }\frac { x }{ 2 } \right) } dx$$ $$\frac { 2x }{ 1+{ x }^{ 2 } }$$ ∫(ax² + bx + c) dx $$\frac { (x+1){ (x+logx) }^{ 2 } }{ x }$$ Solution: tan x + sec x + C, प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए. Ex 7.3 Class 12 Maths Question 6. $$\frac { x+2 }{ \sqrt { { x }^{ 2 }+2x+3 } }$$ ∫(4e3x + 1) dx ∫(ax + b)² dx (b) $$\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 8x-9 }{ 9 } \right) +c$$ $$\frac { x }{ (x+1)(x+2) }$$ Ex 7.2 Class 12 Maths Question 38. Find the following integrals in Exercises 6 to 20 : Ex 7.1 Class 12 Maths Question 6. (b) $$\frac { \pi }{ 12 }$$ sinx sin2x sin3x The Left Hand Rule is not really about using rectangles to approximate area. Solution: Miscellaneous Exercise Class 11 Maths Question 28: $$\frac { cos2x+{ 2sin }^{ 2 }x }{ { cos }^{ 2 }x }$$ Solution: Teaching & Learning Plan: Integral Calculus ... use integration to find the average value of a function over an interval â¢ integrate sums, differences and constant multiples : ... integral calculus. Ex 7.4 Class 12 Maths Question 4. Solution: $$\sqrt { { x }^{ 2 }+3x }$$ Ex 7.3 Class 12 Maths Question 15. (c) $${ e }^{ x }sinx+c$$ Integration questions with answers are available here for students of Class 11 and Class 12. Ex 7.2 Class 12 Maths Question 15. Solution: Ex 7.10 Class 12 Maths Question 3: In this chapter, students learn about integral calculus (definite and indefinite), their properties and much more. Solution: Ex 7.2 Class 12 Maths Question 5. Integration as limit as a sum - We use basic definition of integration, Integration = Area to form limit as a sum formula and then solve its questions Definite Integration - Solving definite integration using methods of indefinite integration, and using properties of definite integration The same is true of our current expression: Z x2 â2 â u du dx dx = Z x2 â2 â udu. Solution: Ex 7.2 Class 12 Maths Question 11. (b) $$\frac { 2\pi }{ 3 }$$ Ex 7.2 Class 12 Maths Question 19. 10 questions on geometric series, sequences, and l'Hôpital's rule with answers. Solution: Ex 7.2 Class 12 Maths Question 2. Solution: हम जानते हैं कि, $$\frac { d }{ dx }$$ sin 3x = 3 cos 3x. Ex 7.4 Class 12 Maths Question 25. $$\frac { 1 }{ x({ x }^{ n }+1) }$$ Solution: Free download NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.11, Ex 7.10, Ex 7.9, Ex 7.8, Ex 7.7, Ex 7.6, Ex 7.5, Ex 7.4, Ex 7.3, Ex 7.2, Ex 7.1 Integrals PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20. Ex 7.10 Class 12 Maths Question 15: = $$\frac { 1 }{ 2 }t-x+c$$ $$\frac { x\quad { cos }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } }$$ ∫(sin 2x -4e3x) dx = ∫sin 2x dx – 4∫e3x …(1), Ex 7.1 Class 11 Maths प्रश्न 6. Examples: 1. â«(3x 2 - 2x + 1) dx 2. â«3e x dx 3. â«4/x dx Solution: Ex 7.9 Class 12 Maths Question 22. $$\int _{ 0 }^{ 5 }{ (x+1)dx }$$ Ex 7.2 Class 12 Maths Question 21. Solution: $$\sqrt { ax+b }$$ x log2x Solution: Solution: Solution: Solution: Ex 7.10 Class 12 Maths Question 19: Solution: Ex 7.10 Class 12 Maths Question 16: (So you should really know about Derivatives before reading more!). Solution: Ex 7.3 Class 12 Maths Question 17. (d) $$\frac { { x }^{ 2 } }{ 2 } \sqrt { 1+{ x }^{ 2 } } +\frac { 1 }{ 2 } { x }^{ 2 }log\left| x+\sqrt { 1+{ x }^{ 2 } } \right| +c$$ Ex 7.4 Class 12 Maths Question 18. Solution: 166 Chapter 8 Techniques of Integration going on. $$\frac { { (x-2)e }^{ x } }{ { (x-1) }^{ 3 } }$$ = ∫(sec² x + sec x tan x) dx Solution: Solution: Ex 7.4 Class 12 Maths Question 1. $$\int _{ 1 }^{ \sqrt { 3 } }{ \frac { dx }{ { 1+x }^{ 2 } } \quad equals }$$ Ex 7.3 Class 12 Maths Question 23. $$x\quad { tan }^{ -1 }x$$ Ex 7.1 Class 12 Maths Question 2. Solution: Solution: Solution: Ex 7.6 Class 12 Maths Question 7. (b) tanx – cotx + c Ex 7.3 Class 12 Maths Question 4. But we don't have to add them up, as there is a "shortcut". (a) $$log\left| \frac { { (x-1) }^{ 2 } }{ x-2 } \right| +c$$ Solution: All common integration techniques and even special functions are supported. Integration is like filling a tank from a tap. Ex 7.10 Class 12 Maths Question 2: Solution: (a) $${ x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } -\frac { 129 }{ 8 }$$ Interactive graphs/plots help â¦ Solution: Choose the correct answer in exercise 23 and 24. Solution: Ex 7.6 Class 12 Maths Question 1. $$\frac { 2cosx-3sinx }{ 6cosx+4sinx }$$ Solution: Ex 7.1 Class 12 Maths Solution: Ex 7.5 Class 12 Maths Question 18. ∫(2x² + ex) dx = 2∫x² dx + ∫ex dx, Ex 7.1 Class 11 Maths प्रश्न 14. But remember to add C. From the Rules of Derivatives table we see the derivative of sin(x) is cos(x) so: But a lot of this "reversing" has already been done (see Rules of Integration). Solution: $$\int { \frac { { sin }^{ 2 }x-{ cos }^{ 2 }x }{ { sin }^{ 2 }x{ cos }^{ 2 }x } } dx\quad is\quad equal\quad to$$ Solution: $${ e }^{ 2x+3 }$$ Ex 7.6 Class 12 Maths Question 13. Solution: Ex 7.2 Class 12 Maths Question 25. Solution: Ex 7.8 Class 12 Maths Question 2. (c) $$-log|x|+\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$$ On Rules of Integration there is a "Power Rule" that says: Knowing how to use those rules is the key to being good at Integration. Solution: Miscellaneous Exercise Class 11 Maths Question 1: $$\int { { \left[ \sqrt { x } -\frac { 1 }{ \sqrt { x } } \right] }^{ 2 }dx }$$ Solution: The Class 12 NCERT Maths Book contains the concept of integrals in chapter 7. Ex 7.1 Class 12 Maths Question 3. Solution: Ex 7.1 Class 12 Maths Question 18. Solution: ∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = I (d) $$\frac { 3 }{ 2 } { x }^{ \frac { 3 }{ 2 } }+\frac { 1 }{ 2 } { x }^{ \frac { 1 }{ 2 } }+c$$ In fact the concept of integration owes its origin to the problem of finding areas of plane regions, surface areas and volumes of solid bodies etc. Solution: Miscellaneous Exercise Class 11 Maths Question 22: Ex 7.1 Class 12 Maths Question 11. Maths Questions and Answers with Full Working on Integration that range in difficulty from easy to hard. हल- Ex 7.2 Class 12 Maths Question 28. (c) -tanx+cotx+c $$\frac { 1 }{ x(logx)^{ m } } ,x>0$$ Solution: $$\sqrt { 1+\frac { { x }^{ 2 } }{ 9 } }$$ { x }) } } dx\quad is\quad equal\quad to\) Solution: Miscellaneous Exercise Class 11 Maths Question 7: Solution: Solution: In this article, we will provide you with NCERT Solutions for Class 12 Maths Chapter 7 – Integrals which have been designed by the best teachers in India. Ex 7.10 Class 12 Maths Question 6: Solution: Miscellaneous Exercise Class 11 Maths Question 25: $$\sqrt { { x }^{ 2 }+4x+1 }$$ Ex 7.2 Class 12 Maths Question 4. $$\frac { 1 }{ { x }^{ 2 }-9 }$$ It is the "Constant of Integration". If $$\frac { d }{ dx } f(x)={ 4x }^{ 3 }-\frac { 3 }{ { x }^{ 4 } }$$ such that f(2)=0 then f(x) is Solution: Ex 7.4 Class 12 Maths Question 10. Solution: Ex 7.10 Class 12 Maths Question 8: ∫(4e3x + 1) dx = 4∫e3xdx + ∫1 dx, Ex 7.1 Class 11 Maths प्रश्न 8. ∫(2x² + ex) dx Solution: Solution: Miscellaneous Exercise Class 11 Maths Question 17: हम जानते हैं कि, $$\frac { d }{ dx }$$ cos2x = -2 sin 2x, Ex 7.1 Class 11 Maths प्रश्न 2. $$\int _{ -1 }^{ 1 }{ { e }^{ x } } dx\quad$$ (d) $${ e }^{ x }tanx+c$$ $$\frac { 1 }{ \sqrt { 8+3x-{ x }^{ 2 } } }$$ $$\frac { { xe }^{ x } }{ { (1+x) }^{ 2 } }$$ Solution: Ex 7.9 Class 12 Maths Question 17. Ex 7.2 Class 12 Maths Question 29. Solution: Solution: Ex 7.10 Class 12 Maths Question 1: Announcements Applying to uni? 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