# Ex 7.10, 10

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex7.10, 10 Choose the correct answer If 𝑓 𝑥= 0𝑥𝑡 sin𝑡 𝑑𝑡, then 𝑓 𝑥 is (A) cos 𝑥+𝑥 𝑠𝑖𝑛 𝑥 (B) 𝑥 𝑠𝑖𝑛 𝑥 (C) 𝑥 cos 𝑥 (D) sin𝑥 𝑥 cos𝑥 If 𝑓 𝑥= 0𝑥𝑡 sin𝑡 𝑑𝑡 Integrating by parts 𝑓 𝑥= 0𝑥𝑡 sin𝑡 𝑑𝑡 By ILATE rule , 𝑡 is first function and sin 𝑡 is second function Hence 0𝑥𝑡 sin𝑡 𝑑𝑡= 𝑡 sin𝑡 𝑑𝑡− 𝑑𝑑𝑡𝑡× sin𝑡 𝑑𝑡 𝑑𝑡0𝑥 = 𝑡× − cos𝑡− 1× cos𝑡 𝑑𝑡 0𝑥 = −𝑡 cos𝑡+ sin𝑡0𝑥 =−𝑥 cos𝑥+ sin𝑥− −0× cos0+ sin0 = sin𝑥−𝑥 cos𝑥 Hence 𝑓 𝑥= sin𝑥−𝑥 cos𝑥 Therefore 𝑓′ 𝑥= 𝑑𝑑𝑥 sin𝑥−𝑥 cos𝑥 = 𝑑𝑑𝑥 sin𝑥− 𝑑𝑑𝑥 𝑥 cos𝑥 = cos𝑥− 𝑥 𝑑( cos𝑥)𝑑𝑥+ cos𝑥 𝑑𝑥𝑑𝑥 = cos𝑥− 𝑥 − sin𝑥+ cos𝑥 = cos𝑥+𝑥 sin𝑥− cos𝑥 =𝑥 sin𝑥 Hence Option B is Correct

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.