Π / 2 ∫ − π / 2 Sin 3 X D X

प्रश्न

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

उत्तर

\[Let I = \int_\frac{- \pi}{2}^\frac{\pi}{2} \sin^3 x d x\]
\[ = \int_\frac{- \pi}{2}^\frac{\pi}{2} \sin x\left( 1 - \cos^2 x \right)dx\]
\[ = \int_\frac{- \pi}{2}^\frac{\pi}{2} \sin x dx - \int_\frac{- \pi}{2}^\frac{\pi}{2} \sin x \cos^2 x dx\]
\[ = \left[ - \cos x \right]_\frac{- \pi}{2}^\frac{\pi}{2} + \left[ \frac{\cos^3 x}{3} \right]_{- \frac{\pi}{2}}^\frac{\pi}{2} \]
\[ = 0 + 0 = 0\]

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Definite Integrals

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 23 Q 22 Q 24

अध्याय 19: Definite Integrals - Exercise 20.5 [पृष्ठ ९५]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12

अध्याय 19 Definite Integrals
Exercise 20.5 | Q 23 | पृष्ठ ९५

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