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NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.2

NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.2

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-7 (Integrals)Exercise 7.2 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.
NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.2

Exercise 7.2

Q1. Integrate the function 2x1+x2.

Answer.  
Q2. Integrate the function 

Answer.  Let log |x| = t , 1xdx=dt 

Q3. Integrate the function

Answer. 1x+xlogx=1x(1+logx) Let 1+logx=t1xdx=dt 

Q4. Integrate the function: sin x ⋅ sin (cos x)

Answer. sin x ⋅ sin (cos x) Let cos x = t ∴ −sin x dx = dt 
Q5. Integrate the function sin (ax + b ) cos ( ax + b )

Answer. sin(ax+b)cos(ax+b)=2sin(ax+b)cos(ax+b)2=sin2(ax+b)2  Let 2(ax+b)=t2adx=dt 

Q6. Integrate the function 

 Let ax+b=tadx=dtdx=1adt 
Q7. Integrate the function xx+2

Answer. Let (x + 2) = t ∴ dx = dt xx+2dx=(t2)tdt=t322t12)dt=t32dt2t12dt 

Q8. Integrate the function 
Answer.  Let 1+2x2=t4xdx=dt 
Q9. Integrate the function: (4x+2)x2+x+1


Answer.  Let x2+x+1=t(2x+1)dx=dt(4x+2)x2+x+1dx (4x+2)x2+x+1dx=2tdt=2tdt 
Q10. Integrate the function : 

Answer. 1xx=1x(x1) Let (x1)=t12xdx=dt 

Q11. Integrate the function : 

Answer. Let x + 4 = t ∴ dx = dt xx+4dx=(t4)tdt=(t4t)dt=t32324(1212)+C 
Q12. Integrate the function: (x31)13x5


Answer.  Let x31=t3x2dx=dt (x31)13x5dx=(x31)13x3x2dx=t13(t+1)dt3=13t43+t13)dt 

Q13. Integrate the function : 

Answer.  Let 2+3x3=t9x2dx=dt 
Q14. Integrate the function : 1x(logx)m,x>0,m1

Answer. Let log x = t 
Q15. Integrate the function : 

Answer.  Let 94x2=t8xdx=dtx94x2dx=181tdt 

Q16. Integrate the function : 
Answer. Let 2x + 3 = t ∴ 2dx = dt