Integral of sin(2x)dx

  1. 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.....
  2. jcsd
  3. Mark44

    Staff: Mentor

    Use substitution, with u = 2x, du = 2dx. Integration by substitution is the reverse of the chain rule in differentiation.
  4. 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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