What is the integral from 0 to t^4 of sqrt(u^3) ?

The integral from 0 to t^4 of sqrt(u^3) is (2t^{10})/5

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integral from 0 to t^4 of sqrt(u^3)

\int_{0}^{t^{4}} u^{3} d u

\frac{2 t ^{10}}{5}

Solution steps

\int_{0}^{t^{4}} u^{3} d u

u^{3} = u^{\frac{3}{2}},

assuming

u \geq 0

= \int_{0}^{t^{4}} u^{\frac{3}{2}} d u

Apply the Power Rule

= [\frac{2}{5} u^{\frac{5}{2}}]_{0}^{t^{4}}

Compute the boundaries:

\frac{2}{5} t^{10}

= \frac{2}{5} t^{10}

Simplify

= \frac{2 t ^{10}}{5}

What is the integral from 0 to t^4 of sqrt(u^3) ?
The integral from 0 to t^4 of sqrt(u^3) is (2t^{10})/5