Find the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0, and x = 3, about the y-axis.
Volume of "disc" at x is \(\pi y^2dx\)
So overall volume = \(\int_0^3\pi x^4dx \rightarrow \pi 3^5/5 \rightarrow 243\pi/5\)
Oops! That's the volume rotated about the x axis!
Volume rotated about the y axis is \(\int_0^9\pi x^2 dy \rightarrow \int_0^9 \pi ydy \rightarrow 81\pi/2\)
