# integral

• Oct 2nd 2006, 11:08 AM
Judi
integral
taking integral from 0 to 1 of x^2/(x^2+1)

I thank you all in advance,
Judi
• Oct 2nd 2006, 11:36 AM
topsquark
Quote:

Originally Posted by Judi
taking integral from 0 to 1 of x^2/(x^2+1)

I thank you all in advance,
Judi

Here's a big hint. (I think this is one of ThePerfectHacker's tricks, but I may be wrong.)

Let the numerator x^2 = x^2 + 1 - 1. Then the fraction becomes:
x^2/(x^2 + 1) = 1 - 1/(x^2 + 1)

You might find the last integral easier to do. (Think trig substitution.)

-Dan
• Oct 2nd 2006, 12:22 PM
Judi
I see how that integral becomes 1-1/(x^2+1)
I see I have to use trig ...I draw some pictures and I don't get it
how do you take integral of 1/(x^2+1)
help...
• Oct 2nd 2006, 12:26 PM
topsquark
Quote:

Originally Posted by Judi
I see how that integral becomes 1-1/(x^2+1)
I see I have to use trig ...I draw some pictures and I don't get it
how do you take integral of 1/(x^2+1)
help...

Let x = tan(theta)
Then dx = sec^2(theta) d(theta)
x^2 + 1 = tan^2(theta) + 1 = sec^2(theta)

So dx/(x^2 + 1) = sec^2(theta) d(theta)/sec^2(theta) = d(theta)

Don't forget to change the limits! (I always do anyway. :) )

-Dan
• Oct 2nd 2006, 04:27 PM
ThePerfectHacker
Quote:

Originally Posted by Judi
how do you take integral of 1/(x^2+1)
help...

It is a tabular integral you need to have it burned in your memory.
It is the arctangent function.
~~~
That is exactly what I would have done topsquark.
• Oct 2nd 2006, 06:34 PM
JakeD
Quote:

Originally Posted by Judi
how do you take integral of 1/(x^2+1)

See The Integrator. It is a resource you should know about.
• Oct 3rd 2006, 04:19 AM
topsquark
Quote:

Originally Posted by JakeD
See The Integrator. It is a resource you should know about.

That is a good resource and I recommend it. However it doesn't show you how to do the integral... :)

-Dan
• Oct 3rd 2006, 04:52 AM
earboth
Quote:

Originally Posted by topsquark
That is a good resource and I recommend it. However it doesn't show you how to do the integral... :)

-Dan

Hi,

I've attached a screen shot: I've "done" this problem with Derive. With this program it is possible to get a solution step by step.

tschüss

EB