What is the integral from 0 to t^4 of sqrt(u^5) ?

The integral from 0 to t^4 of sqrt(u^5) is (2t^{14})/7

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integral from 0 to t^4 of sqrt(u^5)

\int_{0}^{t^{4}} u^{5} d u

\frac{2 t ^{14}}{7}

Solution steps

\int_{0}^{t^{4}} u^{5} d u

u^{5} = u^{\frac{5}{2}},

assuming

u \geq 0

= \int_{0}^{t^{4}} u^{\frac{5}{2}} d u

Apply the Power Rule

= [\frac{2}{7} u^{\frac{7}{2}}]_{0}^{t^{4}}

Compute the boundaries:

\frac{2}{7} t^{14}

= \frac{2}{7} t^{14}

Simplify

= \frac{2 t ^{14}}{7}

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What is the integral from 0 to t^4 of sqrt(u^5) ?
The integral from 0 to t^4 of sqrt(u^5) is (2t^{14})/7