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

The integral from 3 to x^3 of t^3 is (x^{12}-81)/4

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integral from 3 to x^3 of t^3

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

\frac{x ^{12} - 81}{4}

Solution steps

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

Apply the Power Rule

= [\frac{t ^{4}}{4}]_{3}^{x^{3}}

Compute the boundaries:

\frac{x ^{12}}{4} - \frac{81}{4}

= \frac{x ^{12}}{4} - \frac{81}{4}

Simplify

= \frac{x ^{12} - 81}{4}

What is the integral from 3 to x^3 of t^3 ?
The integral from 3 to x^3 of t^3 is (x^{12}-81)/4