- #1

Kqwert

- 160

- 3

## Homework Statement

Hello,

a bowl is created when rotating the function

[tex]f(x) =

\begin{cases}

0, & 0 \leq x \lt 6 \\

(12/\pi)arcsin(x-6), & 6\leq x \leq 7

\end{cases}[/tex]

around the y-axis. Find the height (h) and the volume (V) of the bowl.

## Homework Equations

## 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

[tex]

\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?