1. rotational volume question

Hi all, here's my question:

Find the volume of the solid formed by rotating the region enclosed by
y=e^(2x) + 1, y=0, x=0, x=0.2

My attempt at a solution:
V = pi int{ x = 0 to 0.2} [ (e^(2x) + 1)^2 dx]
V= pi int{ x = 0 to 0.2} [ ( e^(4x) + 2 e^(2x) + 1) dx]
V= pi { x = 0 to 0.2} ( (1/4) e^(4x) + (2/2) e^(2x) + x)
V = pi ( [(1/4) e^(0.8) + e^(0.4) + 0.4] - [(1/4) + 1] )

This isn't the right answer though. I'd like to know what I did wrong so I can get credit here and do problems right in the future. Thanks!!!!!

2. Originally Posted by yeshtikvah
Hi all, here's my question:

Find the volume of the solid formed by rotating the region enclosed by
y=e^(2x) + 1, y=0, x=0, x=0.2

My attempt at a solution:
V = pi int{ x = 0 to 0.2} [ (e^(2x) + 1)^2 dx]
V= pi int{ x = 0 to 0.2} [ ( e^(4x) + 2 e^(2x) + 1) dx]
V= pi { x = 0 to 0.2} ( (1/4) e^(4x) + (2/2) e^(2x) + x)
V = pi ( [(1/4) e^(0.8) + e^(0.4) + 0.4] - [(1/4) + 1] )

This isn't the right answer though. I'd like to know what I did wrong so I can get credit here and do problems right in the future. Thanks!!!!!

All is correct but the last, usually easier, part of evaluation: it must be $\frac{1}{4}e^{0.8}+e^{0.4}+0.2 <<<===$ you put 0.4 instead...that's all the problem!

Tonio

3. Thank you!

Yes, you're right that should have been .2!

I tried that answer, but the online homework still says it's wrong.

This happened with another problem I KNOW i did right. At least I know I'm doing the problems the right way. I guess I'll have to see my teacher to see why our answers aren't giving me any darn credit.

4. Originally Posted by yeshtikvah
Yes, you're right that should have been .2!

I tried that answer, but the online homework still says it's wrong.

This happened with another problem I KNOW i did right. At least I know I'm doing the problems the right way. I guess I'll have to see my teacher to see why our answers aren't giving me any darn credit.
I don't know where some of you guys study that you've to produce your homework ONLINE and/or check it with some online checker or whatever.
Anyway, check your result with a calculator..

Tonio

Ps. Im yesh tikvah az lo hakol avud...