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Math Help - Calculus Question

  1. #1
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    Calculus Question

    84. The base of a solid S is the region enclosed by the graph of y = (lnx)^(1/2), the line x = e, and thex-axis. If the cross sections of S perpendicular to the x-axis are squares, then the volume of S is


    (A)12
    (B)23
    (C) 1
    (D) 2
    (E)13(e3-1)
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  2. #2
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    Quote Originally Posted by frozenflames
    84. The base of a solid S is the region enclosed by the graph of y = (lnx)^(1/2), the line x = e, and thex-axis. If the cross sections of S perpendicular to the x-axis are squares, then the volume of S is


    (A)12
    (B)23
    (C) 1
    (D) 2
    (E)13(e3-1)
    The formula is,
    \int^a_bA(x)dx. Thus, you need to find a function for the area of each cross section A(x). Since, the base is \sqrt{\ln(x)} its height is also that because it forms square cross sections. Since, the area of the square is the sides squared we have A(x)=(\sqrt{\ln x})^2=\ln x. Now find the a,b the problem says from the x-axis until x=e. To find the x-axis find when it is zero. Thus, \sqrt{\ln x}=1 which happens at x=0. Thus,
    V=\int^e_1\ln xdx=1
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