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Math Help - unable to find my mistake with integration

  1. #1
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    unable to find my mistake with integration

    find the arc length of 27y^2 = 4(x-2)^3 from ( 2,0) to (11, 6(3)^(1/2))?

    by differentiation, i got dy/dx = 6 (27)^(1/2) (x-2)^(1/2)

    and forming the integration equation i got,
    integrate ( 972x - 1943) and

    then finding the area form x=11 to x=2, my answer was 39375.

    but the answer is supposed to be 14.

    may i know where i gone wrong?

    thanks!
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    find the arc length of 27y^2 = 4(x-2)^3 from ( 2,0) to (11, 6(3)^(1/2))?

    by differentiation, i got dy/dx = 6 (27)^(1/2) (x-2)^(1/2)
    Apparently you differentiated incorrectly.

    y^2= \frac{4}{27}(x-2)^3 so y= \frac{2}{3\sqrt{3}}(x-2)^{3/2}.

    \frac{dy}{dx}= \frac{(x- 2)^{1/2}}{\sqrt{3}}.

    From that 1+ (dy/dx)^2= 1+ (x-2)^3/3

    and forming the integration equation i got,
    integrate ( 972x - 1943) and

    then finding the area form x=11 to x=2, my answer was 39375.

    but the answer is supposed to be 14.

    may i know where i gone wrong?

    thanks!
    Follow Math Help Forum on Facebook and Google+

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