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. 🙂

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