# Homework Help: Help with an integration by parts problem

1. May 24, 2007

### stanners

integration problem :(

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

int from 1 to 1/4 of [cos(pi*sqrt(t))] / sqrt(t) dt

2. Relevant equations

3. The attempt at a solution
I tried using integration by parts

used u = cos pi (sqrt(t)) and dv = sqrt(t), but got a really messy number as int of vdu

so I tried u = sqrt t, du = 1/2sqrt(t)
dv = cos pi*sqrt(t) , v = sin pi sqrt(t) * pi/2sqrt(t)

So This doesn't seem right, how would I approach this problem?

2. May 25, 2007

### tronter

You want $$\int_{1}^{\frac{1}{4}} \frac{\cos \pi \sqrt{t}}{\sqrt{t}} \; dt$$

3. May 25, 2007

### stanners

Yeah, but integration by parts didn't work, and I don't see how I can use substitution, any help?

4. May 25, 2007

### Reshma

The change of variable method is correct.
Put $u = \sqrt t$
$2du = \frac{dt}{\sqrt t}$
Substituting this will simplify the integrand. However, I think the mistake you are making is; you are forgetting to change the limits(1 & 1/4) of the integral. Whenever you make a variable change, the limits change according to the new variable.

Hope this helps...

5. May 25, 2007

### tronter

multiply numerator and denominator by $$\sqrt{t}$$

You get: $$\int_{1}^{\frac{1}{4}} \frac{\cos \pi t}{t} \; dt$$

6. May 25, 2007

### trajan22

A substitution should work, try u=pi(t)^.5

7. May 25, 2007

### Reshma

Hey, that's wrong :surprised. Multiplying $\sqrt t$ in the numerator doesn't change $\cos \pi \sqrt t$ to $\cos \pi t$.

Last edited: May 25, 2007
8. May 25, 2007

### stanners

Oh wow... haha, yeah.. thanks.

I was using u = cos pi(t)^.5

Bah, thanks.