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

The integral from 0 to pi/2 of sin^2(x is sin^2(d)(pi^2)/8

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integral from 0 to pi/2 of sin^2(x

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

sin^{2} (d) \frac{π ^{2}}{8}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= sin^{2} (d) [\frac{x ^{2}}{2}]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π ^{2}}{8}

= sin^{2} (d) \frac{π ^{2}}{8}

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What is the integral from 0 to pi/2 of sin^2(x ?
The integral from 0 to pi/2 of sin^2(x is sin^2(d)(pi^2)/8