Is there an easier way to solve this integral?

**Ares_D1** · Aug 22nd 2009, 08:07 AM

Sorry, I'm terrible at typing this out using the math code so I'll paste an image:

I've been trying to solve this using parts, but I'm getting nowhere fast. Should I throw some substitution in there also? If someone could show me how to do this one it would be greatly appreciated.

**Rapha** · Aug 22nd 2009, 08:10 AM

Hello Ares_D1!

Originally Posted by Ares_D1

Sorry, I'm terrible at typing this out using the math code so I'll paste an image:

I've been trying to solve this using parts, but I'm getting nowhere fast. If someone could show me how to do this one it would be greatly appreciated.

Here is my suggestion:

substitute z:=x^2

=> z' := 2x and dx = dz/z'

Therefore

$\int -2x^3*e^{-x^2}\pi dx = \int -2x^3*e^{-z}\pi \frac{dz}{2x}$

$=\int -x^2*e^{-z}\pi dz = \int -z*e^{-z}\pi dz$

Yours
Rapha

**o_O** · Aug 22nd 2009, 08:12 AM

Imagine it like this: $\pi\int {\color{blue}-2x} \cdot x^2 \cdot e^{{\color{red}-x^2}} \ {\color{blue}dx}$

So now: ${\color{red}u = -x^2} \ \Rightarrow \ {\color{blue}du = -2x \ dx}$

So your integral becomes: $-\pi\int u e^u du$

which is an easy one by parts.

**Ares_D1** · Aug 22nd 2009, 08:29 AM

Thanks guys, very helpful!

Thread: Is there an easier way to solve this integral?

LinkBack

Thread Tools

Display

Is there an easier way to solve this integral?

Similar Math Help Forum Discussions

some easier probability

It cant get easier than this ...

any better or easier way to solve it ?

Which equation is easier to solve?

maybe an easier one...

Search Tags