What is the integral from 0 to pi/4 of sqrt(x) ?

The integral from 0 to pi/4 of sqrt(x) is (pi^{3/2})/(12)

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integral from 0 to pi/4 of sqrt(x)

\int_{0}^{\frac{π}{4}} x d x

\frac{π ^{\frac{3}{2}}}{12}

Decimal Notation

0.46402 \dots

Solution steps

\int_{0}^{\frac{π}{4}} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{\frac{π}{4}}

= [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{π ^{\frac{3}{2}}}{12}

= \frac{π ^{\frac{3}{2}}}{12}

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What is the integral from 0 to pi/4 of sqrt(x) ?
The integral from 0 to pi/4 of sqrt(x) is (pi^{3/2})/(12)