Help finding the integral

ned13b · 2010-10-24 09:11:50

$205a8e678dd5fa85588375f4454b311.png$

so far I've gotten to

The integral with t as the numerator is giving me trouble. How do I integrate it (using arctan)?

Thanks for the help

ned13b · 2010-10-24 09:35:35

nevermind, i was attacking the problem from completely the wrong angle. got it now

bobbym · 2010-10-24 09:51:00

Hi ned13b;

Welcome to the forum.

Here is the easiest way in the world. Useful for rational functions like this one.

Whenever the numerator is the derivative of the denominator times by a constant then the following formula holds.

Since the derivative of the denominator is 4t + 4 and the numerator is 1/4 of that then a = 1 / 4 and the integral is:

That is for the indefinite integral, now we must handle the intervals of 0 and 1.

Can you do that?

ned13b · 2010-10-24 11:59:40

Thanks, I have another question now that I am stuck on...

im wanting to use

but since if

then which doesnt seem to work because there is no x infront of the e in the original problem?

bobbym · 2010-10-24 13:51:11

Hi;

There is no closed form for that integral in terms of elementary functions. The answer involves the error function.

ned13b · 2010-10-25 14:58:14

Ok, so ive been working on the problem even longer now and still no dice:

The region bounded by

, y=0, x=0, and x=1 is revolved about the y-axis. Find the volume of the resulting solid.

Shouldnt

from y=0 to e^-1=y give the answer? Apparently not, what am I doing wrong?

Math Is Fun Forum