Question

Find the volume of the solid (using washers method) obtained by rotating the region bounded by the curves x=0, y-2, y=square root of x about the y- axis.

Answer 1

Is that y=2 or x=y-2?

Answer 2

y=2

Answer 3

Because it didn't look like y=2, wasnt sure.

Answer 4

Oh ok.

Answer 5

I think washer is \(2\pi r h\), right?

Answer 6

sorry. I am a little confused what should r be equal to?

Answer 7

In this case: \[
r = x\\
h = 2-\sqrt{x}
\]

Answer 8

washers is pi r^2

Answer 9

Oh, ok...

Answer 10

So we're integrating with respect to \(y\) then, right?

Answer 11

\[
r=x=y^2
\]

Answer 12

yes

Answer 13

\[
V = \pi\int_0^2 (y^2)^2\;dy
\]

Answer 14

We use : \[
y=\sqrt x \implies y^2=x
\]

Answer 15

oh, I got my mistake! I used wrong limits! Thanks!

Answer 16

your limits. heh.