Integration by subs. or parts?

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August 22nd 2006, 03:13 AM
sterps

Integration by subs. or parts?

I have this question in a quiz for uni:
http://users.bigpond.net.au/sterps/pictures/int.JPG

They show the exact same question in my lecture notes equalling:

1/2 e^x^2 + C , though im confused on how they get rid of the x in front: xe^x^2

any help would be appreciated
August 22nd 2006, 03:29 AM
topsquark

Quote:

Originally Posted by sterps

I have this question in a quiz for uni:
http://users.bigpond.net.au/sterps/pictures/int.JPG

They show the exact same question in my lecture notes equalling:

1/2 e^x^2 + C , though im confused on how they get rid of the x in front: xe^x^2

any help would be appreciated

$\int dx \, xe^{x^2}$

Let $y = x^2$ , then $dy = 2x dx$

Then
$\int dx \, xe^{x^2} = \int \frac{dy}{2}e^y$

$= \frac{1}{2}e^y + C = \frac{1}{2}e^{x^2} + C$

I don't know of a way to do this using integration by parts because $\int dx \, e^{x^2}$ can't be done exactly.

-Dan
August 22nd 2006, 06:18 AM
CaptainBlack

You can do this without needing to integrate.

Just differentiate (a) through (d), one of these derivatives will be the
integrand, and that will be the correct solution.

RonL
August 22nd 2006, 10:18 AM
Jameson

Quote:

Originally Posted by CaptainBlack

You can do this without needing to integrate.

Just differentiate (a) through (d), one of these derivatives will be the
integrand, and that will be the correct solution.

RonL

Yes, but that doesn't help integrating techniques much :)
August 22nd 2006, 10:35 AM
CaptainBlack

Quote:

Originally Posted by Jameson

Yes, but that doesn't help integrating techniques much :)

It does if it teaches the student that they are allowed to spot the derivative
under the integral sign, or to use the fundamental theorem where they might
not have thought of it.

RonL
August 23rd 2006, 05:20 AM
topsquark

And solving the problem backwards is always a good trick to have when doing multiple choice tests.

-Dan