# Homework Help: Integration by parts computation

1. Oct 26, 2012

### the_kid

1. The problem statement, all variables and given/known data
Consider the following integral:

I=$\int^{\pi/4}_{0}$cos(xt$^{2}$)tan$^{2}$(t)dt

I'm trying to compute as many terms as possible of its asymptotic expansion as x$\rightarrow\infty$.

2. Relevant equations

x

3. The attempt at a solution
Let u=cos(xt$^{2}$). And dv=tan$^{2}$(t)dt.
Then du=-2xtcos(xt$^{2}$)dt and v=$\int$tan$^{2}$(t)dt=tan(t)-t+C.

Integration by parts yields:

I=cos(xt$^{2}$)tan(t)-tcos(xt$^{2}$)+$\int$[2xtcos(xt$^{2}$)tan(t)-2xt$^{2}$cos(xt$^{2}$)]dt,
where all terms are evaluated from 0 to pi/4, obviously.

This feels wrong to me. Can anyone give me some help?

2. Oct 27, 2012

### tiny-tim

hi the_kid!

(try using the X2 button just above the Reply box )
erm

du=-2xtsin(xt2)dt