Out of curiosity:

1. Jan 25, 2009

mathguyz

The calculus book places an emphasis on multiple powers of trig functions in the book. Does anyone here really know what the integral of sin^2dx is? What about the integral of cos^2dx is? I dont think I ve actually ever seen it.

2. Jan 25, 2009

phreak

You can calculate them rather easily if you use $$\sin(x) = \frac{1}{2i}(e^{ix}-e^{-ix})$$ and $$\cos(x) = \frac{1}{2} (e^{ix}+e^{-ix})$$.

3. Jan 25, 2009

rock.freak667

to integrate either cos2x or sin2x with respect to x, the identity:

cos2x=cos2x-sin2x=2cos2x-1=1-2sin2x

Will help

4. Jan 25, 2009

confinement

Integrals involving higher powers of trig functions occur all the time in physics, one example of this occurs when dealing with spherical harmonics, which are a set of special functions that occur in quantum mechanics and electromagnetism. If you have ever seen s,p,d,f orbitals in chemistry, know that the shapes they are showing you correspond to spherical harmonics, and that working with these requires you to integrate higher powers of trigonometric functions.