# Foo - Is this integral correct?

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View Full Version : Is this integral correct?

phantomcow2
09-02-10, 07:57 PM
I'm trying to solve a differential equation but am stuck on a specific step that involves integration. Could someone please explain how the following is true?

http://img121.imageshack.us/img121/3763/integraln.jpg

If we integrate both sides both sides with respect to t, I would have expected the following result:

1/(1+t^2) - 1/(1+1^2)*y = 3*arctan(t) + C

And factoring out the 1/(1+t^2) from the left, we would get [1/(1+t^2)](y-1). Solving for y becomes

-3*arctan(t)*(1+t^2) +1 + C = y

Why am I incorrect?

jccaclimber
09-03-10, 09:36 AM
I'm not 100% sure your wxy Or, xyz statement is true, but I'm not much of a math guy as far as engineers are concerned.

jfmckenna
09-03-10, 10:06 AM
This part of your equation makes no sense: 1/(1+1^2). One would simply write that as 1/2.

jccaclimber
09-03-10, 12:57 PM
That second 1 is a lower case T.

RUOkie
09-03-10, 01:09 PM
I'm pretty sure the answer is 42

or possibly poo

jfmckenna
09-03-10, 03:11 PM
That second 1 is a lower case T.

Looks like a one to me but yeah must have been a typo.

phantomcow2
09-03-10, 04:42 PM
oops, good catch. The one should have been a lower case t. :).

RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.

banerjek
09-03-10, 04:46 PM
RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.
How can you get more general than the answer to life, the universe, and everything?

jsharr
09-03-10, 04:58 PM
oops, good catch. The one should have been a lower case t. :).

RUOkie, 42 couldn't possibly be a valid solution since the solution is a general one -- it doesn't pertain to a specific number.

then it has to be "poo" by process of elimination. next question please.

Greg_R
09-03-10, 06:07 PM
Are you asking how the last line in the image is correct? The integral of d/dt (X) with respect to t = X (integral of a derivative of X = X). That is y/1+t^2 in your example. You already agree with the right side integral solution so now you just need to multiply both sides by 1+t^2 to solve for y.