मराठी

Π / 2 ∫ − π / 2 Sin 3 X D X .

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प्रश्न

\[\int\limits_{- \pi/2}^{\pi/2} \sin^3 x\ dx .\]
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उत्तर

\[Let I = \int_{- \frac{\pi}{2}}^\frac{\pi}{2} \sin^3 x\ d x\]

\[ = \int_{- \frac{\pi}{2}}^\frac{\pi}{2} \sin x \sin^2 x\ dx\]

\[ = \int_{- \frac{\pi}{2}}^\frac{\pi}{2} \sin x\left( 1 - \cos^2 x \right) dx\]

\[Let\ \cos x = t, then - \sin x\ dx = dt, \]

\[When\, x \to - \frac{\pi}{2} ; t \to 0\ and\ x \to \frac{\pi}{2} ; t \to 0\]

\[I = \int_0^0 \left( - 1 + t^2 \right) dt\]

\[\]

\[ = 0\]

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पाठ 19: Definite Integrals - Very Short Answers [पृष्ठ १११]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 19 Definite Integrals
Very Short Answers | Q 5 | पृष्ठ १११

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