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Integration by parts

  1. Oct 31, 2013 #1
    1. The problem statement, all variables and given/known data
    ∫x*cos(x^2) dx

    I tried using integration by parts, but the integral of cos(x^2) is very long, and I couldn't get it completely with my knowledge at the moment, so is there an easier way to solve this problem?
     
  2. jcsd
  3. Oct 31, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, don't use integration by parts. Use u substitution. Put u=x^2.
     
  4. Oct 31, 2013 #3
    So the definite integral [0, sqrt(pi)] would be 0 correct?
     
  5. Oct 31, 2013 #4

    Mark44

    Staff: Mentor

    Yes, correct.
    Also, when you're working with integrals, it's usually best to see if a simple substitution will work before tackling it with integration by parts. Integration by substitution is usually a simpler approach that integration by parts, so if it doesn't work out, you haven't wasted much time.

    In this case, and as you saw, it's a very obvious substitution that works.

    BTW, when you post a problem, you need to show what you have tried, even if it wasn't successful. That's a rule in this forum.
     
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