Calculus

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Volume problem:

y=x^3, x=y^3; rotated about x-axis

I first made y=x^1/3, then x^3=x^1/3

Then I tried to do an integration from 0 to 1 with x^1/3-x^3, but I can't get one of the possible answers, which are:

A. 16/35π
B. 16/7π
C. 18/35
D. 7/2
E. 16π

Any advice?

  • Calculus -

    | = integrate symbol

    y = x^3
    y^3 = x, y = x^(1/3)

    Using the formula
    pi | (f(x))^2 - (g(x))^2 dx

    pi | (x^3)^2 - x^(1/3)^2 dx
    pi | (x^6) - x^(2/3) dx
    pi ( 1/7 x^7 - 3/5 x^(5/3))

    When I evaluated from 0 to 1,
    I got,
    - 16/35 pi

  • Calculus -

    Correction for above,

    | = integrate symbol

    y = x^3
    y^3 = x, y = x^(1/3)

    Using the formula
    pi | (f(x))^2 - (g(x))^2 dx

    pi | x^(1/3)^2 - (x^3)^2 dx
    pi | x^(2/3) - (x^6) dx
    pi ( 3/5 x^(5/3) - 1/7 x^7 )

    When I evaluated from 0 to 1,
    I got,
    16/35 pi

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