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Indefinite Integral

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data


    [tex] \int{ x^3 \sqrt{(36-x^2)}dx} [/tex]

    2. Relevant equations



    3. The attempt at a solution

    I tried using trig substitution but got [tex] 7776\int{cos^3(\theta)-cos^5(\theta)d\theta} [/tex] which seems completely wrong



    [tex]6cos(\theta)=x
    [/tex]
    [tex]6sin(\theta)d\theta=dx
    [/tex]
    [tex]6sin(\theta)=\sqrt{36-x^2}
    [/tex]

    [tex] \int{ (6cos(\theta))^36sin(\theta)6sin(\theta)d\theta [/tex]
     
  2. jcsd
  3. Dec 6, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You have an odd number of "x"s outside the square root so try this: Write the integral as [itex]\int x^2\sqrt{36- x^2}(x dx)[/itex] and let u= 36- x2. Then du= 2x dx so x dx= (1/2)du and [itex]x^2= 36- u[/itex].
     
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