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calculus

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the area under the curve y= square root of 9-x^2 with coordinates x=-3 and 3 , find the volume rotated aroudn the x-axis

  • calculus - ,

    Hey, that's just the top half of the circle
    x^2 + y^2 = 9 rotated, giving us the whole sphere
    radius is 3,so the volume is (4/3)π(3^3) = 36π

    But I guess you want it done using integration....

    volume π∫(9-x^2) dx from -3 to 3
    = π[9x - (1/3)x^3] from -3 to 3
    = π(27 - 9 - (-27 + 9))
    = 36π

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