Integral Calculus Question 364
Question: $ \int_{{}}^{{}}{e^{x}\sin x(\sin x+2\cos x)}\ dx= $
[MP PET 1988]
Options:
A) $ e^{x}{{\sin }^{2}}x+c $
B) $ e^{x}\sin x+c $
C) $ e^{x}\sin 2x+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{e^{x}\sin x(\sin x+2\cos x)dx} $ $ =\int_{{}}^{{}}{e^{x}{{\sin }^{2}}x,dx}+\int_{{}}^{{}}{e^{x}2\sin x,\cos xdx} $ $ =\int_{{}}^{{}}{e^{x}{{\sin }^{2}}x,dx}+\int_{{}}^{{}}{e^{x}\sin 2x,dx} $ $ =e^{x}{{\sin }^{2}}x-\int_{{}}^{{}}{e^{x}\sin 2x,dx}+\int_{{}}^{{}}{e^{x}\sin 2x,dx,+c} $ $ =e^{x}{{\sin }^{2}}x+c. $ Aliter : $ \int_{{}}^{{}}{e^{x}({{\sin }^{2}}x+\sin 2x)dx=e^{x}{{\sin }^{2}}x+c.} $
BETA
