# Thread: Surface area generated by rotating curve around y-axis

1. ## Surface area generated by rotating curve around y-axis

I'm having a spot of trouble with this problem:

Find the surface area generated by rotating the given curve about the y-axis.
x=(e^t)-t
y=4e^(t/2)
0<t<8

My homework is submitted online, and I keep working this problem out but it says I have it wrong, but I'm pretty sure I'm doing it right.

I know A(s) = integral from 0 to 8 of 2pi x(t)sqrt((dx/dt)^2+(dy/dt)^2)dt, but I keep messing up. Help!

...Maybe i'm using the wrong equation?

2. Originally Posted by DarthPipsqueak
I'm having a spot of trouble with this problem:

Find the surface area generated by rotating the given curve about the y-axis.
x=(e^t)-t
y=4e^(t/2)
0<t<8

My homework is submitted online, and I keep working this problem out but it says I have it wrong, but I'm pretty sure I'm doing it right.

I know A(s) = integral from 0 to 8 of 2pi x(t)sqrt((dx/dt)^2+(dy/dt)^2)dt, but I keep messing up. Help!

...Maybe i'm using the wrong equation?
your integral set up is correct ... the surface area I get is quite large (a bit on the side of ridiculous going to t = 8)

$A = \pi(e^{16}-12e^8-69)$

3. I was getting very large numbers too! But this worked out fine, and I was able to figure out the integral. I think I went wrong with my algebra somewhere.

### find the area of the surface generated by revolving the curve about the given axis. (give your answer correct to 1 decimal place.) x=1/2 t^3, y=2 t 1, 1<=t<=2, y-axis

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