What is the integral from 0 to t^8 of sqrt(u^5) ?

The integral from 0 to t^8 of sqrt(u^5) is (2t^{28})/7

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integral from 0 to t^8 of sqrt(u^5)

\int_{0}^{t^{8}} u^{5} d u

\frac{2 t ^{28}}{7}

Solution steps

\int_{0}^{t^{8}} u^{5} d u

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

assuming

u \geq 0

= \int_{0}^{t^{8}} u^{\frac{5}{2}} d u

Apply the Power Rule

= [\frac{2}{7} u^{\frac{7}{2}}]_{0}^{t^{8}}

Compute the boundaries:

\frac{2}{7} t^{28}

= \frac{2}{7} t^{28}

Simplify

= \frac{2 t ^{28}}{7}

What is the integral from 0 to t^8 of sqrt(u^5) ?
The integral from 0 to t^8 of sqrt(u^5) is (2t^{28})/7