# College Math Teaching

## September 20, 2013

### Stupid Integral Tricks….

Filed under: calculus, integrals, integration by substitution — Tags: — collegemathteaching @ 9:35 pm

Ok what is the worst way to perform $\int sin(2x) dx$ correctly?

How about $\int sin(2x)dx = \int 2sin(x)cos(x)dx = sin^2(x) + C$ ?

Yes; if you compare $sin^2(x)$ to the expected $\frac{-1}{2} cos(2x)$ you’ll see that $sin^2(x) = \frac{1}{2} - \frac{1}{2}cos(2x)$. So the answers differ by a constant and therefore correspond to the same indefinite integral.

I wanted so much to take off a point for “style” but didn’t. 🙂