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Math Help - Integral

  1. #1
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    Integral

    Find
    4 f(x) dx
    0

    if f(x) =
    2 for x < 2
    x for x2
    .


    How should I go about starting this type of problem. I'm not sure what deltax would be since they dont give an "n" value.
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  2. #2
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    Re: Integral

    What "n" or "deltax" are you talking about? Does this problem specifically require you to use a "Riemann sum" approximation?

    It should be easy to find the exact value "geometrically". For x= 0 to 2, the graph is a horizontal straight line, y= 2, so the "area under the curve" is the area of a square, 2 high and 2 wide. For x= 2 to 4, the graph is a straight line through (2, 2) and (4, 4). The area under that is the area of a trapezoid with "height" 2 (x= 2 to x= 4) and bases of length 2 (y= 0 to y= 2) and 4 (y= 0 to y= 4). If you don't want to use the formula for area of a trapezoid, note that drawing a horizontal line from (2, 2) to (4,2) divides that trapezoid into a 2 by 2 square and a right triangle with base of length 2 and height 2.
    Thanks from Steelers72
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  3. #3
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    Re: Integral

    Thank you! Making a diagram made this much easier like you said!
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