Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Integration by parts
Ex 7.6, 3
Ex 7.6, 23 (MCQ)
Example 17
Ex 7.6, 1
Ex 7.6, 2 Important
Ex 7.6, 12
Example 21 Important
Ex 7.6, 21
Ex 7.6, 5 Important
Ex 7.6, 4
Ex 7.6, 6
Ex 7.6, 15
Example 18 Important
Ex 7.6, 14 Important
Ex 7.6, 7 Important
Ex 7.6, 9
Ex 7.6, 8
Ex 7.6, 11 You are here
Example 20 Important
Ex 7.6, 13 Important
Ex 7.6, 22 Important
Ex 7.6, 10 Important
Example 38 Important
Integration by parts
Last updated at May 29, 2023 by Teachoo
Ex 7.6, 11 𝑥 cos−1𝑥 1 − 𝑥2 Let cos−1𝑥=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 −1 1 − 𝑥2 = 𝑑𝑡𝑑𝑥 𝑑𝑥=− 1 − 𝑥2 𝑑𝑡 Putting the value of cos−1x = t and dx = − 1− x2 dt , we get 𝑥 cos−1𝑥 1 − 𝑥2 .𝑑𝑥 = 𝑥 . 𝑡 1 − 𝑥2 .𝑑𝑥 = 𝑥 . 𝑡 1 − 𝑥2 . − 1 − 𝑥2𝑑𝑡 = −𝑥𝑡 . 𝑑𝑡 = − 𝑥𝑡 . 𝑑𝑡 = − cos𝑡𝑡 . 𝑑𝑡 = − 𝑡 cos𝑡. 𝑑𝑡 =− 𝑡 cos𝑡. 𝑑𝑡− 𝑑𝑡𝑑𝑡 cos𝑡. 𝑑𝑡𝑑𝑡 =− 𝑡 sin𝑡− 1 . sin𝑡𝑑𝑡 =− 𝑡 sin𝑡− − cos𝑡+𝐶 =− 𝑡 sin𝑡+ cos𝑡+𝐶 =−𝑡 sin𝑡− cos𝑡+𝐶 =−𝑡 1− 𝑐𝑜𝑠2𝑡 −𝑐𝑜𝑠𝑡+𝐶 = − cos−1𝑥 1− 𝑥2−𝑥+𝐶 = − 1− 𝑥2 cos−1𝑥+𝑥+𝐶