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

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

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integral from 0 to pi of sqrt(x)

\int_{0}^{π} x d x

\frac{2 π ^{\frac{3}{2}}}{3}

Decimal

3.71221 \dots

Solution steps

\int_{0}^{π} x d x

Apply the Power Rule

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

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

Compute the boundaries:

π^{\frac{3}{2}} \frac{2}{3}

= π^{\frac{3}{2}} \frac{2}{3}

Simplify

= \frac{2 π ^{\frac{3}{2}}}{3}

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