Integral Calculus Question 409
Question: $ \int_{{}}^{{}}{{{\cos }^{3}}x\ {e^{\log (\sin x)}}}\ dx $ is equal to
Options:
A) $ -\frac{{{\sin }^{4}}x}{4}+c $
B) $ -\frac{{{\cos }^{4}}x}{4}+c $
C) $ \frac{{e^{\sin x}}}{4}+c $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_{{}}^{{}}{{{\cos }^{3}}x{e^{\log \sin x}}dx}=\int_{{}}^{{}}{{{\cos }^{3}}x\sin x,dx} $ $ =-\int_{{}}^{{}}{t^{3}dt}=-\frac{t^{4}}{4}+c=-\frac{{{\cos }^{4}}x}{4}+c $ $ {Putting,t=\cos x] $ .
BETA
