What is the integral from a to b of sqrt(x) ?

The integral from a to b of sqrt(x) is (2b^{3/2}-2a^{3/2})/3

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integral from a to b of sqrt(x)

\int_{a}^{b} x d x

\frac{2 b ^{\frac{3}{2}} - 2 a ^{\frac{3}{2}}}{3}

Solution steps

\int_{a}^{b} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{a}^{b}

= [\frac{2}{3} x^{\frac{3}{2}}]_{a}^{b}

Compute the boundaries:

\frac{2}{3} b^{\frac{3}{2}} - \frac{2}{3} a^{\frac{3}{2}}

= \frac{2}{3} b^{\frac{3}{2}} - \frac{2}{3} a^{\frac{3}{2}}

Simplify

= \frac{2 b ^{\frac{3}{2}} - 2 a ^{\frac{3}{2}}}{3}

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What is the integral from a to b of sqrt(x) ?
The integral from a to b of sqrt(x) is (2b^{3/2}-2a^{3/2})/3