Answer
$\displaystyle \frac{1}{2}\pi r^{2}$
Work Step by Step
Using the same sketch as in the previous exercise,
we conclude that, by replacing 49=$7^2$ with $r^{2}$ in the expression for f(x),
and the bounds from $-r $ to $r$,
we would have a semicircle of radius r.
So,
$A=\displaystyle \frac{1}{2}\pi r^{2}$
$A=\displaystyle \int_{-r}^{r}\sqrt{r^{2}-x^{2}}dx=\frac{1}{2}\pi r^{2}$.