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NCERT Solutions Class 12 Maths Chapter-7 (Integrals)Exercise 7.11

NCERT Solutions Class 12 Maths Chapter-7 (Integrals)Exercise 7.11

NCERT Solutions Class 12 Maths from class 12th Students will get the answers of Chapter-7 (Integrals)Exercise 7.11 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 7.11

Exercise 7.11 

Q1. By using the properties of definite integrals, evaluate the integral. 0π2cos2xdx

Answer. I=0π2cos2xdx ……..(1) I=0π2cos2(π2x)dx(0af(x)dx=0af(ax)dx) I=0π2sin2xdx ………..(2) 

Q2. By using the properties of definite integrals, evaluate the integral. 

Answer. 0π2sinxsinx+cosxdx Let I=0π2sinxsinx+cosxdx.......(1) I=0π2sin(π2x)sin(π2x)+cos(π2x)dx(0af(x)dx=0af(ax)dx) I=0π2coscos+sinxdx......(2) 

Q3. By using the properties of definite integrals, evaluate the integral. 0π2sin32xdxsin32x+cos32x

Answer. Let I=0π2sin32xsin32x+cos32xdx..(1) I=0π2sin32(π2x)sin32(π2x)+cos32(π2x)dx(0af(x)dx=0af(ax)dx) I=0π2cos32xsin32x+cos32xdx.....(2) Adding (1) and (2), we obtain 

Q4. By using the properties of definite integrals, evaluate the integral. 

Answer. LetI=0π2cos5xsin5x+cos5xdx......(1) I=0π2cos5(π2x)sin5(π2x)+cos5(π2x)dx(0af(x)dx=0af(ax)dx) I=0π2sin5xsin5x+cos5xdx.....(2) 

Q5. By using the properties of definite integrals, evaluate the integral. 

Answer. I=55|x+2|dx It can be seen that (x+2) 0 on [5,2] and (x+2)0 on [2,5] I=52(x+2)dx+25(x+2)dx(abf(x)=acf(x)+cbf(x)) I=[x22+2x]52+[x22+2x]25 =[(2)22+2(2)(5)222(5)]+[(5)22+2(5)(2)222(2)] 

Q6. By using the properties of definite integrals, evaluate the integral. 28|x5|dx

Answer.  Let I=26|x5|dx It can be seen that (x5)0 on [2,5] and (x5)0 on [5,8] I=2s(x5)dx+2s(x5)dx(abf(x)=atf(x)+cbf(x)) 

Q7. By using the properties of definite integrals, evaluate the integral. 01x(1x)ndx

Answer.  Let I=01x(1x)ndxI=01(1x)(1(1x))ndx =01(1x)(x)ndx=01(xnxn+1)dx =[xn+1n+1xn+2n+2]01(10f(x)dx=10f(ax)dx) 

Q8. By using the properties of definite integrals, evaluate the integral. 0π4log(1+tanx)dx

Answer. I=0π4log(1+tanx)dx.....(1) I=0π4log[1+tan(π4x)]dx(0af(x)dx=0af(ax)dx)