What is the integral from 0 to t^4 of sqrt(u^7) ?

The integral from 0 to t^4 of sqrt(u^7) is (2t^{18})/9

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integral from 0 to t^4 of sqrt(u^7)

\int_{0}^{t^{4}} u^{7} d u

\frac{2 t ^{18}}{9}

Solution steps

\int_{0}^{t^{4}} u^{7} d u

u^{7} = u^{\frac{7}{2}},

assuming

u \geq 0

= \int_{0}^{t^{4}} u^{\frac{7}{2}} d u

Apply the Power Rule

= [\frac{2}{9} u^{\frac{9}{2}}]_{0}^{t^{4}}

Compute the boundaries:

\frac{2}{9} t^{18}

= \frac{2}{9} t^{18}

Simplify

= \frac{2 t ^{18}}{9}

What is the integral from 0 to t^4 of sqrt(u^7) ?
The integral from 0 to t^4 of sqrt(u^7) is (2t^{18})/9