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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \cos (\sin x)dx$

$(a)\;\frac{\pi x}{2}-x+c \\(b)\;\frac{\pi x}{2}+\frac{x^2}{2}+c \\(c)\;\frac{\pi x}{2}-\frac{x^3}{2}+c \\ (d)\;\frac{\pi x}{2}-\frac{x^2}{2}+c$

1 Answer

We know $\cos ^{-1} x =\large\frac{\pi}{2}$$ - \sin ^{-1}(x)$
=>$\int \large\frac{\pi}{2}$$ -\sin ^{-1} (\sin x)dx$
=> $\large\frac{ \pi}{2} $$x-\large\frac{x^2}{2} $$+c$
Hence d is the correct answer.
answered Jan 2, 2014 by meena.p
 
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