Definite Integration Question 410
Question: $ \int _{1/4}^{1/2}{\frac{dx}{\sqrt{x-x^{2}}}=} $
[SCRA 1986]
Options:
A) $ \pi $
B) $ \frac{\pi }{2} $
C) $ \frac{\pi }{3} $
D) $ \frac{\pi }{6} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int _{1/4}^{1/2}{\frac{dx}{\sqrt{x-x^{2}}}=\int _{1/4}^{1/2}{\frac{dx}{\sqrt{{{( \frac{1}{2} )}^{2}}-{{( x-\frac{1}{2} )}^{2}}}}}}=[ {{\sin }^{-1}}( \frac{\frac{2x-1}{2}}{1/2} ) ] _{1/4}^{1/2} $
$ =[{{\sin }^{-1}}(2x-1)] _{1/6}^{1/2}=\pi /6 $ .
BETA
