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Write a Value of ∫ E Log S I N X Cos X D X

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प्रश्न

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]
योग
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उत्तर

Let Ielog sin x . cos x dx 

\[\int\] sin x × cos x dx            \[\left( \because e^{log \text{ a} }= a \right)\]
Let sin t
⇒​ cos x dx = dt
\[\therefore I\]\[\int\] t . dt

\[= \frac{t^2}{2} + C\]
\[ = \frac{\sin^2 x}{2} + C \left( \because t = \sin x \right)\]

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अध्याय 18: Indefinite Integrals - Very Short Answers [पृष्ठ १९७]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 18 Indefinite Integrals
Very Short Answers | Q 11 | पृष्ठ १९७

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