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Math Help - Integrating Areas/Volumes

  1. #1
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    Integrating Areas/Volumes

    Can someone please help me with problem 3:

    http://www.math.rutgers.edu/~greenfi...dfstuff/w1.pdf


    I can obviously sketch R and for the area, I just need to do a top minus bottom type deal, but I don't get parts b) and c).
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  2. #2
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    Quote Originally Posted by zhupolongjoe View Post
    Can someone please help me with problem 3:

    http://www.math.rutgers.edu/~greenfi...dfstuff/w1.pdf


    I can obviously sketch R and for the area, I just need to do a top minus bottom type deal, but I don't get parts b) and c).
    a) R = \int_{-1}^1 1 - x^2 \, dx


    b) each cross section has area = 4x^2 = 4y

    volume of a square-sided cross section is dV = 4y \cdot dy

     <br />
V = \int_0^1 4y \, dy<br />

    c) area of an equilateral triangle of side s is \frac{\sqrt{3}}{4}s^2

    s = 2x

     <br />
V = \frac{\sqrt{3}}{4} \int_0^1 4y \, dy<br />
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