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

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

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integral from 1 to x of (t^2)

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

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

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

Simplify

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

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