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Ex 7.6
Ex 7.6, 2 Important
Ex 7.6, 3
Ex 7.6, 4
Ex 7.6, 5 Important
Ex 7.6, 6
Ex 7.6, 7 Important
Ex 7.6, 8
Ex 7.6, 9
Ex 7.6, 10 Important
Ex 7.6, 11 You are here
Ex 7.6, 12
Ex 7.6, 13 Important
Ex 7.6, 14 Important
Ex 7.6, 15
Ex 7.6, 16
Ex 7.6, 17
Ex 7.6, 18 Important
Ex 7.6, 19
Ex 7.6, 20 Important
Ex 7.6, 21
Ex 7.6, 22 Important
Ex 7.6, 23 (MCQ)
Ex 7.6, 24 (MCQ) Important
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