If f ( x ) = x , g ( x ) = sin x , then ∫ f ( g ( x )) d x is equal to

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If $f(x)=x, g(x)=\sin x$, then $\int f(g(x)) d x$ is equal to

MathematicsIndefinite IntegrationMHT CETMHT CET 2010

Options:

A $\sin x+c$
B $-\cos x+c$
C $\frac{x^{2}}{2}+c$
D $x \sin x+c$

Solution:

2548 Upvotes Verified Answer

The correct answer is: $-\cos x+c$

$\begin{aligned} \int f(g(x)) d x &=\int f(\sin x) d x \\ &=\int \sin x d x \\ &=-\cos x+c \end{aligned}$

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