Definite Integration Question 376
Question: $ \int_0^{\pi /2}{\frac{\sin x\cos x}{1+{{\sin }^{4}}x}dx=} $
[AISSE 1988]
Options:
A) $ \frac{\pi }{2} $
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{6} $
D) $ \frac{\pi }{8} $
Show Answer
Answer:
Correct Answer: D
Solution:
Put $ {{\sin }^{2}}x=t\Rightarrow dt=2\sin x\cos xdx $
Now $ \int_0^{\pi /2}{\frac{\sin x\cos x}{1+{{\sin }^{4}}x}dx=\frac{1}{2}\int_0^{1}{\frac{1}{1+t^{2}}dt=\frac{1}{2}[{{\tan }^{-1}}t]_0^{1}=\frac{\pi }{8}}} $ .
BETA
