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

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

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

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

\frac{63 π}{512}

Decimal Notation

0.38656 \dots

Solution steps

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

Apply Integral Reduction

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

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

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

Simplify

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

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

Compute the boundaries:

0

= - 0 + \frac{63 π}{512}

Simplify

= \frac{63 π}{512}

\frac{\partial}{\partial y} (- 4 x y + x^{4} + y^{4})

x \to 0 + lim ((sin (x))^{2 x})

\int_{1}^{3} ln (x) d x

\frac{\partial}{\partial x} (e^{- a x})

\frac{d}{d x} (x^{2} + y^{2} - 25)

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