Re: Separation of Variables

Hmm...

$\displaystyle \int e^{-z} dz = -e^{-z} $

You can't do that w substitution as you will get $\displaystyle dw =e^{z} dz $ but there is no $\displaystyle e^{z} $ in the integral to cancel it out

Re: Separation of Variables

I would agree that you should just use the result given by jgv115 but you *can* use the substitution.

You should end up with $\displaystyle \displaystyle \int \frac{1}{w^2}dw$

Re: Separation of Variables

Quote:

Originally Posted by

**a tutor** I would agree that you should just use the result given by jgv115 but you *can* use the substitution.

You should end up with $\displaystyle \displaystyle \int \frac{1}{w^2}dw$

You can use the result IF you mutliply the top and bottom by $\displaystyle \displaystyle \begin{align*} e^z \end{align*}$ first.

Re: Separation of Variables

Quote:

Originally Posted by

**Prove It** You can use the result IF you mutliply the top and bottom by $\displaystyle \displaystyle \begin{align*} e^z \end{align*}$ first.

I see, you need to multiply by 1 before it works..:p

Re: Separation of Variables

Re: Separation of Variables

I'm sorry. I am still not sure what substitution to use. How would I end up with my substitution as 1/w^{2 }??

Re: Separation of Variables

Quote:

Originally Posted by

**NeedsHelpPlease** I'm sorry. I am still not sure what substitution to use. How would I end up with my substitution as 1/w^{2 }??

$\displaystyle \displaystyle \int \frac{1}{w^2}dw$ is not your substitution it is the result of doing the substitution you started.

You had $\displaystyle w=e^z$

so

$\displaystyle dw=e^z \ dz$

and then

$\displaystyle \displaystyle \int \frac{1}{e^z}dz=\int \frac{1}{w}\frac{dw}{w}=\int\frac{1}{w^2}dw $

Re: Separation of Variables

Quote:

Originally Posted by

**a tutor** $\displaystyle \displaystyle \int \frac{1}{w^2}dw$ is not your substitution it is the result of doing the substitution you started.

You had $\displaystyle w=e^z$

so

$\displaystyle dw=e^z \ dz$

and then

$\displaystyle \displaystyle \int \frac{1}{e^z}dz=\int \frac{1}{w}\frac{dw}{w}=\int\frac{1}{w^2}dw $

$\displaystyle \displaystyle = \int{w^{-2}\,dw}$, which should be easy to integrate...