# Definite integral question

1. May 7, 2012

### jd12345

1. The problem statement, all variables and given/known data
Find the value of ∫ ( sin 37x / sin x )dx - from 0 to π

2. Relevant equations

3. The attempt at a solution
Well i tried doing it by parts but it makes its more complicated. I tried to expand sin 37x as sin(36+1)x but could not solve it. I am lost

2. May 7, 2012

### Ray Vickson

$$\sin(nx) = \frac{1}{2i} ( X^n - Y^n), \text{ where } X = e^{ix}, \: Y = 1/X.$$
Thus, $\sin(nx) = \sin(x) [X^{n-1} + X^{n-2}Y + \cdots + Y^{n-1}],$ so
$$\sin(nx)/\sin(x) = X^{n-1} + X^{n-2}Y + \cdots + Y^{n-1}.$$

RGV