a bowl is created when rotating the function
0, & 0 \leq x \lt 6 \\
(12/\pi)arcsin(x-6), & 6\leq x \leq 7
around the y-axis. Find the height (h) and the volume (V) of the bowl.
The Attempt at a Solution
So, I graphed the problem and found the height to be 6 (maximum y-value from the arcsin function). Apparently this is wrong. Why?
For the volume, I considered the integrals
\int_0^6 2\pi(6-0)x \, dx[/tex] and [tex]2\pi \int_6^7 (2/\pi)arcsin(x-6)x \, dx[/tex]
and then adding them together. Where did I go wrong?