Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = ln 3x, y = 4, y = 6, x = 0; about the y-axis

I cant seem to get the integration right, here is what I have so far:

y=ln3x
e^y=3x
1/3 e^y=x
pi/3 integral from 4 to 6 of (e^y)^2
I checked my answer on wolfram, and got the same integral, so it must be a problem with my setup.

Answer 1

Hey Shall I ?

Answer 2

Please, I'm still stuck

Answer 3

Well I don't know integration but see this This is from yahoo I would be glad if it helps

Answer 4

Well if you think about it; the clue is in the axis of rotation. It's rotated around the y-axis and not the x-axis as usual; as well as this; the limits of integration are y-values; so this should tell you that a function of y needs of be integrated; not a function of x.

So instead of π∫ y^2 dx; the formula we have to use is; π∫ x^2 dy

So now we need x in terms of y. Easy enough:

y = ln(3x)

e^y = 3x

x = (1/3)e^y

So then x^2 = (1/9)e^2y

So what we're integrating here is:

π∫ x^2 dy = π∫ (1/9)e^2y dy between the limits of 2 and 6. I'm sure you can mange that :)

Answer 5

Ah, I think I loved the 1/3 out of the integral before squaring it.

Answer 6

Hey I have a site for u to practice do u want it ?

Answer 7

Yeah, sure

Answer 8

http://mathpost.asu.edu/~zinzer/266HW7_Sol.pdf

Answer 9

Nice! thanks

Answer 10

Welcome

Answer 11

Hey thank u for givin me a medal do u understand it now ?

Answer 12

Yeah, it was a careless mistake, I got it right now. I pulled out the 1/3 before i squared it.

Answer 13

OK

Answer 14

And the site?

Answer 15

It it useful.

Answer 16

r u from india

Answer 17

No, USA

Answer 18

ok