Learn how to solve problems step by step online. Integrate the function 1/2(r^2-x^2) from -r to r. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Expand the integral \int_{-r}^{r}\left(r^2-x^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the product \frac{1}{2}\left(\int_{-r}^{r} r^2dx+\int_{-r}^{r}-x^2dx\right). The integral \frac{1}{2}\int_{-r}^{r} r^2dx results in: r^{3}.

Integrate the function 1/2(r^2-x^2) from -r to r