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March 25, 2017

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The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the x-axis. Each cross section perpendicular to the base and the x-axis is a square. Find the volume of the solid.

  • calculus - ,

    Each cross section (from x=0 to x=1) is a square of side √x.

    So the total volume is the area of the square times dx, or A(x)dx

    V=∫ (√x)^2dx from x=0 to 1
    =∫ xdx
    =[x²/2] from 0 to 1
    = 1/2

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