What is the integral from 0 to x^3 of t^2 ?

The integral from 0 to x^3 of t^2 is (x^9)/3

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integral from 0 to x^3 of t^2

\int_{0}^{x^{3}} t^{2} d t

\frac{x ^{9}}{3}

Solution steps

\int_{0}^{x^{3}} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{0}^{x^{3}}

= [\frac{t ^{3}}{3}]_{0}^{x^{3}}

Compute the boundaries:

\frac{x ^{9}}{3}

= \frac{x ^{9}}{3}

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\int_{0}^{1} \frac{1}{( 4 x - 1 ) ^{3}} d x

What is the integral from 0 to x^3 of t^2 ?
The integral from 0 to x^3 of t^2 is (x^9)/3