What is the integral from 0 to t^2 of sqrt(u) ?

The integral from 0 to t^2 of sqrt(u) is (2t^3)/3

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integral from 0 to t^2 of sqrt(u)

\int_{0}^{t^{2}} u d u

\frac{2 t ^{3}}{3}

Solution steps

\int_{0}^{t^{2}} u d u

Apply the Power Rule

= [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{t^{2}}

Compute the boundaries:

\frac{2}{3} t^{3}

= \frac{2}{3} t^{3}

Simplify

= \frac{2 t ^{3}}{3}

What is the integral from 0 to t^2 of sqrt(u) ?
The integral from 0 to t^2 of sqrt(u) is (2t^3)/3