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NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.6

NCERT Solutions Class 12 maths Chapter-7 (Integrals)Exercise 7.6

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-7 (Integrals)Exercise 7.6 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 7.6

Exercise 7.6

Q1. Integrate the function :

Answer. Let I=xsinxdx Taking x as first function and sin x as second function and integrating by parts, we obtain I=xsinxdx{(ddxx)sinxdx}dx 

Q2. Integrate the function :

Answer. Let I=xsin3xdx Taking x as first function and sin 3x as second function and integrating by parts, we obtain I=xsin3xdx{(ddxx)sin3xdx} 

Q3. Integrate the function :x2ex

Answer. Let I=x2exdx Taking x2 as first function and ex as second function and integrating by parts, we obtain I=x2exdx{(ddxx2)exdx}dx=x2ex2xexdx=x2ex2xexdx Again integrating by parts, we obtain 

Q4. Integrate the function :

Answer. Let I=xlogxdx Taking log x as first function and x as second function and integrating by parts, we obtain 

Q5. Integrate the function :

Answer. Let I=xlog2xdx Taking log 2x as first function and x as second function and integrating by parts, we obtain 

Q6. Integrate the function :x2logx

Answer. Let I=x2logxdx Taking log x as first function and x2 as second function and integrating by parts, we obtain 

Q7. Integrate the function :xsin1x

Answer. Let I=xsin1xdx Taking sin1x as first function and x as second function and integrating by parts, we obtain I=sin1xxdx{(ddxsin1x)xdx}dx =sin1x(x22)11x2x22dx =x2sin1x2+12x21x2dx=x2sin1x2+12{1x21x211x2}dx =x2sin1x2+12{1x211x2}dx=x2sin1x2+12{1x2dx11x2dx}=x2sin1x2+12{x21x2+12sin1xsin1x}+C=x2sin1x2+x41x2+14sin1x12sin1x+C 

Q8. Integrate the function :xtan1x

Answer. Let I=xtan1xdx Taking tan1x as first function and x as second function and integrating by parts, we obtain I=tan1xxdx{(ddxtan1x)xdx}dx=tan1x(x22)11+x2x22dx=x2tan1x212x21+x2dx 

Q9. Integrate the function :

Answer. Let I=xcos1xdx Taking  as first function and x as second function and integrating by parts, we obtain I=cos1xxdx{(ddxcos1x)xdx}dx=cos1xx2211x2x22dx=x2cos1x2121x211x2dx=x2cos1x212{1x2+(11x2)}dx=x2cos1x2121x2dx12(11x2)dx =x2cos1x212I112cos1x where, I1=1x2dxI1=x1x2ddx1x2xdxI1=x1x22x21x2xdx