# Homework Help: Integration by expansion

1. Apr 18, 2014

### wel

Consider the integral

I(x)= \frac{1}{\pi} \int^{\pi}_{0} sin(xsint) dt

show that

I(x)= 4+ \frac{2x}{\pi}x +O(x^{3})

as $x\rightarrow0$.

=> I Have used the expansion of McLaurin series of $I(x)$ but did not work.

(Note: It is not my homework or coursework question but it is from past exam paper which i am preparing for my exam)

2. Apr 18, 2014

### Simon Bridge

Maclearen series: $$f(t)=\sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}x^n$$

$f(t)=\sin(x\sin t),\; f(0)=0$

$f'(t)=\cdots$

$f''(t)=\cdots$

etc. until you start getting terms in x3

3. Apr 19, 2014

### Staff: Mentor

wel,
Physics Forums rules require that you show what you have tried. I sent you a PM about this, and am closing this thread. You are welcome to start a new thread for this problem, but you need to show what you have tried.