Question

Evaluate: \(\int_0^3 \sqrt{9 - x^2} \, dx\).

Hint:

Geometry shortcut: \(\int_0^r \sqrt{r^2 - x^2} \, dx\) is simply the area of a quadrant of a circle, which is \(\frac{1}{4} \pi r^2\). Here \(r=3\), so Area \(= \frac{1}{4} \pi (3)^2 = \frac{9\pi}{4}\). This is much faster than integration!

Answer 1