Definite Integration Question 109

Question: The value of $ \int_0^{n\pi +v}{|\sin x|dx} $ is

[IIT 1994]

Options:

A) x $ 2n+1+\cos v $

B) $ 2n+1-\cos v $

C) $ 2n+1 $

D) $ 2n+\cos v $

Show Answer

Answer:

Correct Answer: B

Solution:

$ \int_0^{n\pi +v}{|\sin x|dx=\int_0^{n\pi }{|\sin x|dx+\int _{n\pi }^{n\pi +v}{|\sin x|dx}}} $

$ =2n+1-\cos v $ .