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Definite Integral as Limit of Sum

∫cos x ·cossi...

Question

$\int cos x \cdot cos (sin x) d x$ is equal to
(where $C$ is constant of integration)

A

cos (sin x) + C

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B

sin (sin x) + C

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C

sin (cos x) + C

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D

cos (cos x) + C

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Solution

The correct option is B $sin (sin x) + C$
$I = \int cos x \cdot cos (sin x) d x$
Putting $sin x = t$
$\Rightarrow cos x d x = d t$
$∴ I = \int cos t d t = sin t + C = sin (sin x) + C$

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Definite Integral as Limit of Sum

Standard XII Mathematics

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