What is the integral from 0 to pi/2 of sqrt(x) ?

The integral from 0 to pi/2 of sqrt(x) is (pi^{3/2})/(3sqrt(2))

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integral from 0 to pi/2 of sqrt(x)

\int_{0}^{\frac{π}{2}} x d x

\frac{π ^{\frac{3}{2}}}{3 2}

Decimal

1.31246 \dots

Solution steps

\int_{0}^{\frac{π}{2}} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{\frac{π}{2}}

= [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{\frac{π}{2}}

Compute the boundaries:

\frac{π ^{\frac{3}{2}}}{3 2}

= \frac{π ^{\frac{3}{2}}}{3 2}

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What is the integral from 0 to pi/2 of sqrt(x) ?
The integral from 0 to pi/2 of sqrt(x) is (pi^{3/2})/(3sqrt(2))