What is the integral from 3 to x of t^7 ?

The integral from 3 to x of t^7 is (x^8-6561)/8

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integral from 3 to x of t^7

\int_{3}^{x} t^{7} d t

\frac{x ^{8} - 6561}{8}

Solution steps

\int_{3}^{x} t^{7} d t

Apply the Power Rule

: [\frac{t ^{8}}{8}]_{3}^{x}

= [\frac{t ^{8}}{8}]_{3}^{x}

Compute the boundaries:

\frac{x ^{8}}{8} - \frac{6561}{8}

= \frac{x ^{8}}{8} - \frac{6561}{8}

Simplify

= \frac{x ^{8} - 6561}{8}

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What is the integral from 3 to x of t^7 ?
The integral from 3 to x of t^7 is (x^8-6561)/8