NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.1

NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.1

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-7 (Integrals)Exercise 7.1 This chapter will help you to learn the basics and you should expect at least one question in your exam from this chapter.
We have given the answers of all the questions of NCERT Board Mathematics Textbook in very easy language, which will be very easy for the students to understand and remember so that you can pass with good marks in your examination.
Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.1
NCERT Question-Answer

Class 12 Mathematics

Chapter-7 (Integrals)

Questions and answers given in practice

Chapter-7 (Integrals)

Exercise 7.1

Q1. Find an anti-derivative (or integral) of the following functions by the method of inspection. sin 2x

Answer. The anti derivative of sin 2x is a function of x whose derivative is sin 2x. It is known that, ddx(cos2x)=2sin2xsin2x=12ddx(cos2x)sin2x=ddx(12cos2x) Therefore, the anti derivative of 

Q2. Find an anti derivative (or integral) of the following functions by the method of inspection. cos 3x

Answer.  The anti derivative of cos 3x is a function of x whose derivative is cos 3x. It is known that, ddx(sin3x)=3cos3xcos3x=13ddx(sin3x)cos3x=ddx(13sin3x) Therefore, the anti derivative of cos3x is 13sin3x.

Q3. Find an anti derivative (or integral) of the following functions by the method of inspection. e2x


Answer. The anti derivative of e2x is the function of x whose derivative is e2x. It is known that, ddx(e2x)=2e2xe2x=12ddx(e2x)e2x=ddx(12e2x) Therefore, the anti derivative of e2x is 12e2x

Q4. Find an anti derivative (or integral) of the following functions by the method of inspection. 

Answer. The anti derivative of (ax+b)2 is the function of x whose derivative is (ax+b)2. It is known that ddx(ax+b)3=3a(ax+b)2(ax+b)2=13addx(ax+b)3(ax+b)2=ddx(13a(ax+b)3) Therefore, the anti derivative of 

Q5. Find an anti derivative (or integral) of the following functions by the method of inspection: 

Answer. The anti derivative of sin2x4e3x is the function of x whose derivative is sin2x4e3x. It is known that, ddx(12cos2x43e3x)=sin2x4e3x Therefore, the anti derivative of (sin2x4e3x) is (12cos2x43e3x).

Q6. Find the following integral 

Answer. 

Q7. Find the following integral 
Answer. 

Q8. Find the following integral (ax2+bx+c)dx


Answer. 

Q9. Find the following integral (2x2+ex)dx


Answer. 

Q10. Find the following integral 
Answer. 
Q11. Find the following integral 

Answer. 

Q12. Find the following integral 

Answer. 

Q13. Find the following integral 
Answer. 

Q14. Find the following integral 

Answer. 

Q15. Find the following integral 

Answer. x(3x2+2x+3)dx=(3x52+2x32+3x12)dx=3x52dx+2x32dx+3x12dx 

Q16. Find the following integral 

Answer. 

Q17. Find the following integral (2x23sinx+5x)dx



Answer. (2x23sinx+5x)dx 

Q18. Find the following integral 

Answer. 

Q19. Find the following integral 

Answer. sec2xcsc2xdx 

Q20. Find the following integral 23sinxcos2xdx


Answer. 

Q21. The anti derivative of (x+1x) equals. (A) 13x13+2x12+C (B) 23x23+12x2+C (C) 23x32+2x12+C (D) 32x32+12x12+C


Answer. (x+1x)dx=x12dx+x12dx=x3232+x1212+C=23x32+2x12+C Hence, the correct Answer is C.


Q22. If ddxf(x)=4x33x4 such that f(2)=0. Then f(x) (A) x4+1x31298 (B) x3+1x4+1298 (C) x4+1x3+1298 (D) x3+1x41298


Answer.  It is given that, ddxf(x)=4x33x4 Anti derivative of 4x33x4=f(x) f(x)=4x33x4dxf(x)=4x3dx3(x4)dxf(x)=4(x44)3(x33)+Cf(x)=x4+1x3+C  Also, f(2)=0f(2)=(2)4+1(2)3+C=016+18+C=0C=(16+18)C=1298 

Chapter-7 (integrals)