What is the integral from 2 to x of t^6 ?

The integral from 2 to x of t^6 is (x^7-128)/7

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integral from 2 to x of t^6

\int_{2}^{x} t^{6} d t

\frac{x ^{7} - 128}{7}

Solution steps

\int_{2}^{x} t^{6} d t

Apply the Power Rule

: [\frac{t ^{7}}{7}]_{2}^{x}

= [\frac{t ^{7}}{7}]_{2}^{x}

Compute the boundaries:

\frac{x ^{7}}{7} - \frac{128}{7}

= \frac{x ^{7}}{7} - \frac{128}{7}

Simplify

= \frac{x ^{7} - 128}{7}

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What is the integral from 2 to x of t^6 ?
The integral from 2 to x of t^6 is (x^7-128)/7