Integration with Trigonometric Substitution

  1. [SOLVED] Integration with Trigonometric Substitution

    1. The problem statement, all variables and given/known data

    Given integral (I):
    I[(x)sqrt(9-x^2)dx]

    by words:
    Integral of "X" times square root of "9-X(squared)

    Use proper trigonometric substitution to solve this problem.
    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. You don't even need Trig substitution.

    [tex]\int x\sqrt{9-x^2}dx[/tex]

    [tex]u=9-x^2[/tex]
    [tex]du=-2xdx \rightarrow xdx=-\frac 1 2 du[/tex]
     
  4. I know that I don't need that.
    But the problem is, I have to use it.
    The exercise require it.
     
  5. Well you posted the solution to it? I don't know what else to tell you. Just analyze what they did. Work it yourself a couple times if you have to.
     
  6. You forgot a term when you first did the substitution.

    x = 3sin(u)
    dx = 3cos(u)du

    (9 - x^2)^(1/2) = 3cos(u)

    So the integral becomes 27sin(u)cos^2(u)du
     
  7. [tex]\int x^2\sqrt{9-x^2}dx[/tex]
    apropo
    [tex]u=x^2\sqrt{9-x^2}dx[/tex]
     
    Last edited: Mar 3, 2008
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