What is the integral from 1 to x^2 of t^2 ?

The integral from 1 to x^2 of t^2 is (x^6-1)/3

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integral from 1 to x^2 of t^2

\int_{1}^{x^{2}} t^{2} d t

\frac{x ^{6} - 1}{3}

Solution steps

\int_{1}^{x^{2}} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{1}^{x^{2}}

= [\frac{t ^{3}}{3}]_{1}^{x^{2}}

Compute the boundaries:

\frac{x ^{6}}{3} - \frac{1}{3}

= \frac{x ^{6}}{3} - \frac{1}{3}

Simplify

= \frac{x ^{6} - 1}{3}

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What is the integral from 1 to x^2 of t^2 ?
The integral from 1 to x^2 of t^2 is (x^6-1)/3