# Integration sines and cosines question

1. Mar 18, 2004

### ilikephysics

Express the sines and cosines in exponential form and integrate to show that (integral from -pi to pi) sin(3x)cos(4x)dx=0

What I'm thinking is that I should use sin x=e^x-e^-x/2 and cos x=e^x+e^-x/2. And I should multiply sin times 3 and cos times 4 and integrate. And get something like this:

(e^3pi+e^-3pi/2 * e^4pi-e^-4pi/2) - (e^-3pi+e^3pi/2 * e^-4pi-e^4pi/2)=0

I don't think this is right though. Can someone help please?

2. Mar 18, 2004

Try looking up and using some trig reduction formulas.

3. Mar 19, 2004

### HallsofIvy

Staff Emeritus
Yes, I would be inclined to use "reduction formulas" but if the problem specifically said "Express the sines and cosines in exponential form", then the way ilikephysics is approaching this is correct.

However, the formulas are wrong!

$$sin(x)= \frac{e^{ix}-e^{-ix}}{2i}$$
$$cos(x)= \frac{e^{ix}+e^{-ix}}{2}$$

ilikephysics forgot the "i"s.