Question

The region R bounded by the curve 4y=x² and the lines x=4, y=1. Find the volume of the solid formed when R is rotated completely about (b) the y-axis (c) the line y=1(d) the line x=4


the answers should be (b) 18pi (c) 76pi/15 (d)10pi/3

Answer 1

graph http://assets.openstudy.com/updates/attachments/53be7bf6e4b09e08a1c63a82-kira_yamato-1404993364732-screenshot20140710at7.45.15am.png

Answer 2

Something is wrong in here.
\[
x=2\sqrt{y}\\
\begin{align*}
\pi\int_0^1(2\sqrt{y})^2dy&=4\pi\int_0^1y\,dy\\
&=2\pi(y^2)|^1_0\\
&=2\pi
\end{align*}
\]
How do you get \(18\pi\)?

Answer 3

@Callisto Help!

Answer 4

it should be x^2=4y

Answer 5

then looking at the graph the limits of integration are 1 to 4

Answer 6

To me, for b) you should break it into 2 parts: \(\int_0^2 f(x) dx)) + volume of the cylinder washer from 2 to 4