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Math Help - [SOLVED] Volume of a Solid Revolution

  1. #1
    yummycalc
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    [SOLVED] Volume of a Solid Revolution

    I am having trouble with volumes using the definite integral. I wanted to place a couple of questions from my textbook. I was wondering does anyone have any good tips. I have never been good at visualizing volumes even if I sketch the graph on the paper. If anyone could help me I would really appreciate it. Here are two examples from my textbook:

    Region bounded by square root of x, y= 2 and x= 0 about (a) the y-axis; (b) x=1

    y= e^x, x = 0, x = 2 and y = 0 about (a) the y-axis; (b) y = -2. Estimate numerically.

    Thanks very much.
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  2. #2
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    Quote Originally Posted by yummycalc
    Region bounded by square root of x, y= 2 and x= 0 about (a) the y-axis; (b) x=1
    Okay you have the following graph handdrawn below.

    The point where the graphs intersect is at,
    x=4.
    You can look at the graph or solve,
    \sqrt{x}=2--->by squaring both sides.

    Thus, you are going to subtract from area of top curve the area of bottom curve.
    \mbox{Top curve: }y=2
    \mbox{Bottom curve: }y=\sqrt{x}

    Now you take the are from 0\leq x\leq 4
    Finally by the volume of revolution you need to square and multiply by \pi thus,
    The integral is,
    \pi \int_0^4 \left( 2-\sqrt{x})^2 dx
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