Integral Calculus Question 213
Question: If m is an integer, then $ \int_0^{\pi }{\frac{\sin (2mx)}{\sin x}dx} $ is equal to:
Options:
A) 1
B) 2
C) 0
D) $ \pi $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Use $ \int_0^{a}{f(x)dx=\int_0^{a}{f(a-x)dx}} $ $ \int_0^{\pi }{\frac{\sin 2mx}{\sin x}dx=\int_0^{\pi }{\frac{\sin (2m\pi -2mx)}{\sin (\pi -x)}}dx} $ $ =\int_0^{\pi }{\frac{-\sin 2mx}{\sin x}dx=-I\Rightarrow 2I=0\Rightarrow I=0} $
BETA
