Homework Help: Hard definite integration by parts question, need help

1. Jun 24, 2012

limelightdevo

1. The problem statement, all variables and given/known data

Integral, from 0 to 1, y/(e^2y)

2. Relevant equations
Use integration by parts

3. The attempt at a solution

I need integration by parts. The answer is 1/4-3/5e^-2. But I got 1/2 and it all makes sense to me, so tell me what I got wrong.

I put u=e^2y
du=2e^2y

dv= 1/e^2y dy (did u substitution on 2y here)
v=1/2 * ln(e^2y) (here I canceled ln and e, so left with 2y)
v=1/2 * 2y = y

Plugged them into integration by parts formula
and got y^2-(y^2)/2. Plugged in 1 and 0.
And I got 1-1/2 = 1/2. How is this wrong?? I don't understand.

Last edited: Jun 24, 2012
2. Jun 24, 2012

1MileCrash

Your integration of dv is wrong.

3. Jun 24, 2012

SammyS

Staff Emeritus
What is it that you're trying to integrate? What you wrote is ambiguous.

$\displaystyle \int_0^1 \frac{y}{e^{2y}}\,dy\,,$

or

$\displaystyle \int_0^1 y\,e^{2y}\,dy\,,$

or something else?

4. Jun 24, 2012

Staff: Mentor

In addition to what 1MileCrash said, you aren't doing integration by parts correctly. If you integral is $\int ye^{-2y}dy$
then you can't have u = e2y and dv = 1/(e2y)* dy.
Whatever you choose for u and dv, they have to multiply to make your original integrand. In your case u*dv = e2y/e2y * dy = 1 dy, not ye-2ydy.

5. Jun 24, 2012

1MileCrash

So your choice of u and dv should be very clear. As for which one is u and which one is dv - weigh which one will result in a simpler function when differentiated, and try that for u.

6. Jun 24, 2012

limelightdevo

It is y divided by e^2y dy

7. Jun 24, 2012

Staff: Mentor

That's what I understood it to be.

You should write this not as a fraction, but as ye-2ydy.