# Ex 7.5, 16 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

Ex 7.5

Ex 7.5, 1

Ex 7.5, 2

Ex 7.5, 3 Important

Ex 7.5, 4

Ex 7.5, 5

Ex 7.5, 6 Important

Ex 7.5, 7 Important

Ex 7.5, 8

Ex 7.5, 9 Important

Ex 7.5, 10

Ex 7.5, 11 Important

Ex 7.5, 12

Ex 7.5, 13 Important

Ex 7.5, 14 Important

Ex 7.5, 15

Ex 7.5, 16 Important You are here

Ex 7.5, 17

Ex 7.5, 18 Important

Ex 7.5, 19

Ex 7.5, 20 Important

Ex 7.5, 21 Important

Ex 7.5, 22 (MCQ)

Ex 7.5, 23 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 7.5, 16 1 +1 [Hint: multiply numerator and denominator by xn 1 and put xn = t] We can write integrand as 1 + 1 = 1 + 1 1 1 = 1 + 1 = 1 + 1 Let t = Then = 1 Therefore 1 + 1 = 1 + 1 . 1 = 1 n + 1 We can write the integrand as 1 + 1 = + + 1 1 + 1 = + 1 + + 1 By cancelling denominator 1 = + 1 + Putting t = 0 in (1) 1 = 0+1 + 0 1 = = 1 Similarly putting t = 1 in (1) 1 = 1+1 + 1 1 = 0 1 = = 1 Therefore we can write 1 + 1 = 1 1 + 1 Thus, + 1 = 1 1 + 1 = log log +1 + C = log + 1 + Putting back t = 1 + 1 = + +