Integral Calculus Question 188
Question: What is $ \int{{e^{lnx}}\sin xdx} $ equal to (Where $c$ is a constant of integration)?
Options:
A) $ {e^{lnx}}(\sin x-\cos x)+c $
B) $ (\sin x-x\cos x)+c $
C) $ (x\sin x+\cos x)+c $
D) $ (\sin x+x\cos x)-c $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let $ I=\int{{e^{In,x}}\sin xdx=\int{x\sin xdx(\because {e^{\log ,a}}=a)}} $ $ =-x\cos x+\int{1.\cos xdx=(\sin x-x\cos x)+c} $
BETA
