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Integral of sin(2x)dx

by physx_420
Tags: -cos(x), differentation, integral, sin(x)
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Apr4-10, 09:09 PM
P: 33
1. The problem statement, all variables and given/known data
[tex]\int[/tex] sin(2x)dx

2. Relevant equations
I know the integral of sin(x)dx = -cos(x) + C

3. The attempt at a solution
What I did was to say that the integral is -cos(2x) +C, which isn't the correct answer...I should have gotten -1/2(cos(2x)) +C. I can see that this is the correct answer when I differentiate it via chain rule and get sin(2x), however I can't seem to integrate the problem to get the right answer. Can someone walk me through it please.....
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Apr4-10, 09:35 PM
P: 21,214
Use substitution, with u = 2x, du = 2dx. Integration by substitution is the reverse of the chain rule in differentiation.
Apr4-10, 09:49 PM
P: 33
ah so that's where I went wrong....I tried u substitution but I used u=sin2x instead of u=2x. thanks mark44.

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