What is the integral from 0 to pi/2 of cos^2(s)inx ?

The integral from 0 to pi/2 of cos^2(s)inx is (pi^2incos^2(s))/8

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integral from 0 to pi/2 of cos^2(s)inx

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

\frac{π ^{2} in cos ^{2} ( s )}{8}

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos^{2} (s) in \cdot \int_{0}^{\frac{π}{2}} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{\frac{π}{2}}

= cos^{2} (s) in [\frac{x ^{2}}{2}]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π ^{2}}{8}

= cos^{2} (s) in \frac{π ^{2}}{8}

Simplify

= \frac{π ^{2} in cos ^{2} ( s )}{8}

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What is the integral from 0 to pi/2 of cos^2(s)inx ?
The integral from 0 to pi/2 of cos^2(s)inx is (pi^2incos^2(s))/8