What is the integral from 0 to x^2 of t^{3/2} ?

The integral from 0 to x^2 of t^{3/2} is (2x^5)/5

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integral from 0 to x^2 of t^{3/2}

\int_{0}^{x^{2}} t^{\frac{3}{2}} d t

\frac{2 x ^{5}}{5}

Solution steps

\int_{0}^{x^{2}} t^{\frac{3}{2}} d t

Apply the Power Rule

: [\frac{2}{5} t^{\frac{5}{2}}]_{0}^{x^{2}}

= [\frac{2}{5} t^{\frac{5}{2}}]_{0}^{x^{2}}

Compute the boundaries:

\frac{2}{5} x^{5}

= \frac{2}{5} x^{5}

Simplify

= \frac{2 x ^{5}}{5}

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What is the integral from 0 to x^2 of t^{3/2} ?
The integral from 0 to x^2 of t^{3/2} is (2x^5)/5