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Math Help - Calculus Problem

  1. #1
    Junior Member R3ap3r's Avatar
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    Calculus Problem

    Find the approximate area between the curve y = 12x - 2x^2 and the x-axis, from x = 0 to x=5 using 5 inscribed rectangles of equal width.

    My Work:

    n = 5

    y = 12x - 2x^2

    x = 0\; y_0 = 0

    x = 1\; y_1 = 10

    x = 2\; y_2 = 16

    x = 3\; y_3 = 18

    x = 4\; y_4 = 16

    x = 5\; y_5 = 10

    .5h[(y_0 + y_n) + 2(y_1 + y_2 +\; ...\; y_{n - 1})]

    .5\cdot .5[(0 + 10) + 2(10 + 16 + 18 + 16)] = 32.5

    area\; is\; 32.5\; units^2

    Hows it look?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by R3ap3r View Post
    Find the approximate area between the curve y = 12x - 2x^2 and the x-axis, from x = 0 to x=5 using 5 inscribed rectangles of equal width.

    My Work:

    n = 5

    y = 12x - 2x^2

    x = 0\; y_0 = 0

    x = 1\; y_1 = 10

    x = 2\; y_2 = 16

    x = 3\; y_3 = 18

    x = 4\; y_4 = 16

    x = 5\; y_5 = 10

    .5h[(y_0 + y_n) + 2(y_1 + y_2 +\; ...\; y_{n - 1})]

    .5\cdot .5[(0 + 10) + 2(10 + 16 + 18 + 16)] = 32.5

    area\; is\; 32.5\; units^2

    Hows it look?
    I don't understand why you multiplied by 1/2 twice on the outside. It seems to me the area should be 65 by that method, not 32.5.
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  3. #3
    Junior Member R3ap3r's Avatar
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    I c. How would you solve this problem?
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  4. #4
    MHF Contributor
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    Quote Originally Posted by R3ap3r View Post
    I c. How would you solve this problem?
    I like your method, I just don't understand why you multiplied by 1/2 twice on the outside. It seems you are doing something along the lines of

    A = \frac{y_n + y_{n+1}}{2} for the area of each rectangle. Am I correct in this assumption?
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  5. #5
    Junior Member R3ap3r's Avatar
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    well my friend and i plugged in .5 for h. is that wrong?

    this is the trapezium rule btw
    Last edited by R3ap3r; April 27th 2008 at 02:44 PM.
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  6. #6
    Junior Member R3ap3r's Avatar
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    Here's a good page about it maybe you can tell me if what I did is wrong

    The Trapezium Rule
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  7. #7
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    Quote Originally Posted by R3ap3r View Post
    Here's a good page about it maybe you can tell me if what I did is wrong

    The Trapezium Rule
    Where'd you get .5 for h from? It looks like your h (width of each section) should be 1.
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  8. #8
    Junior Member R3ap3r's Avatar
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    hmmm howd i miss that. you are correct thanks.
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