Definite Integration Question 31
Question: The value of $ \int_0^{2\pi }{|{{\sin }^{3}}\theta |d\theta } $ is
[Roorkee Qualifying 1998]
Options:
A) 0
B) $ 3/8 $
C) $ 8/3 $
D) $ \pi $
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ 2\int\limits_0^{\pi }{{{\sin }^{3}}\theta }d\theta =2\int\limits_0^{\pi }{\frac{(3\sin \theta -\sin 3\theta )}{4}}d\theta $
$ =\frac{1}{2}[ -3\cos \theta +\frac{\cos 3\theta }{3} ]_0^{\pi }=\frac{1}{2}[ -3(-1-1)+\frac{(-1-1)}{3} ]=\frac{8}{3} $ .
BETA
