Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Π / 2 ∫ − π / 2 Sin 9 X D X - Mathematics

Sum

\[\int\limits_{- \pi/2}^{\pi/2} \sin^9 x dx\]

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Solution

\[\int_\frac{- \pi}{2}^\frac{\pi}{2} \sin^9 x d x\]

\[\text{Let }f(x) = \sin^9 x\]

\[\text{Consider, }f(-x) = \sin^9 \left( - x \right) = - \sin^9 x = - f\left( x \right)\]

Thus f(x) is an odd function

Therefore,

\[ \int_\frac{- \pi}{2}^\frac{\pi}{2} \sin^9 x d x = 0\]

Concept: Definite Integrals Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 20 Definite Integrals
Revision Exercise | Q 34 | Page 122
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