What is the integral from-r to r of x^2 ?

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

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integral from-r to r of x^2

\int_{- r}^{r} x^{2} d x

\frac{2 r ^{3}}{3}

Solution steps

\int_{- r}^{r} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{- r}^{r}

= [\frac{x ^{3}}{3}]_{- r}^{r}

Compute the boundaries:

2 \cdot \frac{r ^{3}}{3}

= 2 \cdot \frac{r ^{3}}{3}

Simplify

= \frac{2 r ^{3}}{3}

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