Definite Integration Question 15
Question: The value of $ \int_0^{2\pi }{{{\cos }^{99}}xdx} $ is
Options:
A) 1
B) $ -1 $
C) 99
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ I=\int_0^{2\pi }{{{\cos }^{99}}xdx.} $
Then $ I=2\int_0^{\pi }{{{\cos }^{99}}xdx,{\because {{\cos }^{99}}(2\pi -x)={{\cos }^{99}}x}} $
Now, $ \int_0^{\pi }{{{\cos }^{99}}xdx=0,{\because {{\cos }^{99}}(\pi -x)=-{{\cos }^{99}}x}} $
$ \therefore I=2\times 0=0 $ .
BETA
