Integral Calculus Question 419
Question: If $ \int{\sqrt{2}\sqrt{1+\sin x}}dx=-,4\cos (ax+b)+c $ then the value of (a, b) is
[UPSEAT 2002]
Options:
A) $ \frac{1}{2},,\frac{\pi }{4} $
B) $ 1,,\frac{\pi }{2} $
C) 1, 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int{\sqrt{2}\sqrt{1+\sin x}},dx $ $ =\sqrt{2}\int{( \sin \frac{x}{2}+\cos \frac{x}{2} ),dx} $ $ =2\int{\sin ( \frac{\pi }{4}+\frac{x}{2} ),dx=-,4\cos ,( \frac{x}{2}+\frac{\pi }{4} )+c} $ On comparing, $ a=\frac{1}{2},,b=\frac{\pi }{4}. $
BETA
