Volumes of Revolution Math Example 1

Solution

1. 1
   Use the disc method for revolution about the $x$-axis: $V = \pi\int_a^b [f(x)]^2\,dx$. Since $f(x) = \sqrt{x}$, $[f(x)]^2 = x$.
2. 2
   Set up the integral: $$V = \pi\int_0^4 x\,dx$$
3. 3
   Evaluate: $$V = \pi\left[\frac{x^2}{2}\right]_0^4 = \pi\cdot\frac{16}{2} = 8\pi$$