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Math Help - Volume of Solids

  1. #1
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    Exclamation Volume of Solids

    Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^{x/2}. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.

    The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x). Find the volume of this solid.

    How do I do this problem?
    Last edited by summermagic; April 27th 2009 at 06:38 PM.
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    Quote Originally Posted by summermagic View Post
    Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^{x/2}. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g.

    The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y=f(x) to y=g(x). Find the volume of this solid.

    How do I do this problem?
    A = \frac{\pi}{2} r^2

    r = \frac{f(x) - g(x)}{2}

    V = \int_a^b A(x) \, dx
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