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Math Help - Integ.

  1. #1
    Junior Member bebrave's Avatar
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    Integ.

    Hello,
    sorry i cant learn latex
    0 to (2sgrt3)S(sgrt(16-x^2)-2)dx=?
    S=integ.

    i want to see solution way then i can solve ...Thanks for all help
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by bebrave View Post
    Hello,
    sorry i cant learn latex
    0 to (2sgrt3)S(sgrt(16-x^2)-2)dx=?
    S=integ.

    i want to see solution way then i can solve ...Thanks for all help

    \int_0^{2\sqrt{3}}\left(\sqrt{16-x^2} - 2\right)dx=\int_0^{2\sqrt{3}}\left(\dfrac{16-x^2}{\sqrt{16-x^2}} - 2\right)dx =  \int_0^{2\sqrt{3}}\left(\dfrac{16}{\sqrt{16-x^2}}-\dfrac{\frac12 x \cdot 2x}{\sqrt{16-x^2}} - 2\right)dx =

    The first quotient will give an arcsin-function, the second quotient has to be integrated by partial integration and integration by substitution.
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  3. #3
    Junior Member bebrave's Avatar
    Joined
    Apr 2009
    Posts
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    i think this way,
    x=4sint-->dx=4cost.dt
    x=0==>sint=0==>t=0
    x=2sgrt3==>sint=(sgrt3)/2==>t=x/3
    so
    0 to pi/3 S(sgrt(16-16sin^2t)-2)4cost.dt
    0 to pi/3 S(4cost-2)4cost.dt
    0 to pi/3 S(16cos^2t-8cost)dt
    then
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