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Integral by Trig Substitution, Calc 2

  1. Sep 6, 2012 #1
    1. The problem statement, all variables and given/known data
    The definite integral of ∫(x^2 √(a^2-x^2) dx from 0 to a


    2. Relevant equations



    3. The attempt at a solution

    So i don't need actual help with this problem. I got the answer, (π*a^4)/16 and I verified with the back of the book. The question I have is whether this problem merits an entire side of work? None of the examples my professor has given have ever been more than a few lines of work and this took me a whole side of a paper. Am I being inefficient or should I just expect this from now on?

    Oh and sorry if my notation bad or if this should be on another thread, this is my first post lol .__.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 6, 2012 #2

    LCKurtz

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    I guess it amounts to how much you write. It requires a trig substitution followed by a double angle formula. Is that how you did it? Did you carry the limits along with the substitution or did you back substitute to x? That takes more steps. I used about 1/2 of one side of a standard sheet of paper for it.
     
  4. Sep 7, 2012 #3
    I decided to back substitute into x, i thought converting the limits would be a hassle on this question. I think my issue was getting a sin4θ and not knowing any quick identities to simplify. Oh well, thanks for the response
     
  5. Sep 7, 2012 #4

    ehild

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    You could have changed the integration limits after substitution. If you substituted x/a=sin(u) then the integral with respect to u goes from 0 to pi/2.

    ehild
     
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