What is the integral from 0 to pi/2 of cos^{10}(x) ?

The integral from 0 to pi/2 of cos^{10}(x) is (63pi)/(512)

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integral from 0 to pi/2 of cos^{10}(x)

\int_{0}^{\frac{π}{2}} cos^{10} (x) d x

\frac{63 π}{512}

Decimal

0.38656 \dots

Solution steps

\int_{0}^{\frac{π}{2}} cos^{10} (x) d x

Apply Integral Reduction

= [\frac{sin ( x ) cos ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \int_{0}^{\frac{π}{2}} cos^{8} (x) d x

\int_{0}^{\frac{π}{2}} cos^{8} (x) d x = \frac{35 π}{256}

= [\frac{sin ( x ) cos ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \frac{35 π}{256}

Simplify

[\frac{sin ( x ) cos ^{9} ( x )}{10}]_{0}^{\frac{π}{2}} + \frac{9}{10} \cdot \frac{35 π}{256} : [\frac{1}{10} cos^{9} (x) sin (x)]_{0}^{\frac{π}{2}} + \frac{63 π}{512}

= [\frac{1}{10} cos^{9} (x) sin (x)]_{0}^{\frac{π}{2}} + \frac{63 π}{512}

Compute the boundaries:

0

= 0 + \frac{63 π}{512}

Simplify

= \frac{63 π}{512}

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What is the integral from 0 to pi/2 of cos^{10}(x) ?
The integral from 0 to pi/2 of cos^{10}(x) is (63pi)/(512)