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U substitution

  1. Feb 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Im looking over the notes in my lecture and the prof wrote,
    [tex] \int_{0}^{2} \pi(4x^2-x^4)dx=\frac{64\pi}{15} [/tex]
    Im wondering whats the indefinite integral of this equation.

    2. Relevant equations
    using u substitution


    3. The attempt at a solution
    [tex] \int \pi(4x^2-x^4)dx= \pi \int x^2(4-x^2)dx \\
    u = 4 - x^2 \ \ \ \ \ \ \ \ \ \
    -\frac {1}{2} du =xdx \\
    [/tex]

    Im confuse since i have an x^2 but my du=x.

    I attempted to also use from u to get,
    [tex]
    x=\sqrt{4-u} \\
    \pi \int \frac{1}{2}u\sqrt{4-u}dx
    [/tex]
    but it seems this made the formula harder to integrate...or am i just giving up too quickly
     
  2. jcsd
  3. Feb 28, 2016 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    You are making this far too complicated.

    What is ##\int x^n dx##, (for ##n \geq 1##)?
     
  4. Feb 28, 2016 #3
    That makes sense...

    I was working on a bunch of u sub equations earlier. I guess I was on a u sub mode

    Thanks a lot!
     
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