What is the integral from a to r of r^2 ?

The integral from a to r of r^2 is (r^3-a^3)/3

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integral from a to r of r^2

\int_{a}^{r} r^{2} d r

\frac{r ^{3} - a ^{3}}{3}

Solution steps

\int_{a}^{r} r^{2} d r

Apply the Power Rule

= [\frac{r ^{3}}{3}]_{a}^{r}

Compute the boundaries:

\frac{r ^{3}}{3} - \frac{a ^{3}}{3}

= \frac{r ^{3}}{3} - \frac{a ^{3}}{3}

Simplify

= \frac{r ^{3} - a ^{3}}{3}

What is the integral from a to r of r^2 ?
The integral from a to r of r^2 is (r^3-a^3)/3