# Thread: Surface Area obtained by rotating the curve

1. ## Surface Area obtained by rotating the curve

Hi,

My problem is: Find the area of the surface obtained by rotating the curve $x = 5 e^{2y}$ from y=0 to y = 2 about the y-axis.

I use the surface Formula: $S = \int_a^b {2 \pi x} \sqrt{1+{x'}^2} dy$

but could do no more after plug in ${x'} = 10e^y$

Could anyone help me with this? THANKS!!

2. $x' = 10e^{2y}$

This is the second time today I have corrected this error. Someone must be teaching it wrong.

P.S. How is Provo these days?

3. Originally Posted by TKHunny
$x' = 10e^{2y}$

This is the second time today I have corrected this error. Someone must be teaching it wrong.

P.S. How is Provo these days?
right, it should be $x' = 10e^{2y}$,

but problem is actually that I don't know how to deal with:

$\int 2 \pi 5e^{2y} \sqrt{1+100e^{4y}} dy$ after I applied the surface area formula to this question.

4. If you resist the temptation to evaluate the square under the radical, a convenient substitution may come to mind.

$u = 10\cdot e^{2y}$ perhaps? Mind you, it's still not pretty. That's why we invented approximation techniques. Just one of these can be a total bear.