Definite Integration Question 378
Question: $ \int_0^{\pi /4}{{{\tan }^{6}}x{{\sec }^{2}}xdx=} $
[BIT Ranchi 1981]
Options:
A) $ \frac{1}{7} $
B) $ \frac{2}{7} $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ t=\tan x\Rightarrow dt={{\sec }^{2}}xdx $
Now $ \int_0^{\pi /4}{{{\tan }^{6}}x{{\sec }^{2}}xdx=\int_0^{1}{t^{6}dt=\frac{1}{7}[t^{7}]_0^{1}=\frac{1}{7}}} $ .
BETA
