Answer
$\displaystyle \frac{49\pi}{2}$
Work Step by Step
Sketching the function
$f(x)=\sqrt{49-x^{2}},$ bounds: x=$-7$ to x=$7$.
(see below)
We see a semicircle, radius 7,
$A=\displaystyle \frac{1}{2}\pi r^{2}=\frac{1}{2}\pi(7)^{2}=\frac{49\pi}{2}$
$A=\displaystyle \int_{-7}^{7}\sqrt{49-x^{2}}dx=\frac{49\pi}{2}$
