Definite Integration Question 118
Question: If $ \int _{\sin x}^{1}{t^{2}f(t)\ dt=1-\sin x} $ , $ x\in ( 0,\frac{\pi }{2} ) $ then $ f\ ( \frac{1}{\sqrt{3}} ) $ equal to
[IIT Screening 2005]
Options:
A) 3
B) $ \frac{1}{3} $
C) $ \frac{1}{\sqrt{3}} $
D) $ \sqrt{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
On differentiating both sides, we get $ -{{\sin }^{2}}x\ f(\sin x)\cos x=-\cos x $
therefore $ f(\sin x)=\frac{1}{{{\sin }^{2}}x} $
therefore $ f(x)=\frac{1}{x^{2}} $
therefore $ f\ ( \frac{1}{\sqrt{3}} )=3 $ .
BETA
