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Math Help - find area under the curve using calculus

  1. #1
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    find area under the curve using calculus

    hi
    how are u all
    i have a math problem that require from
    me to find area under the curve
    but because am not good in math i didn't
    understand how to find the expresion in the blue
    rectangle
    in the attached pic


    upload picture

    any help
    is appreciated ...


    secondly ...to make sure i will understand this
    type of problems and how to solve it,
    could any one plz solve for me the problem
    below(find tha area under curve)
    and thanks in advance

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  2. #2
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    Re: find area under the curve using calculus

    There is no 'finding' (i- 1/n)\Delta x, that is an arbitrary choice. Once you have divided the interval 0 to 1 in n subintervals, each having length \Delta x, and so right endpoints \Delta x, 2\Delta x, 3\Delta x, ..., i\Delta x, ..., you must choose one x in each interval. Here they have just chosen the simplest- the midpoint: i\Delta x+ (1/2)\Delta x= (i+ 1/2)\Delta x. You could as easily have chosen (i+ 1/4)\Delta x or (i+ 1/3)\Delta x or (i+3/4)\Delta x, etc.

    In the last problem, all of the individual areas are rectangles or trapezoids. Do you know the formulas for area of a rectangle or trapezoid? Find the area of each and add them.
    Last edited by HallsofIvy; August 22nd 2012 at 02:56 AM.
    Thanks from abdi
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  3. #3
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    Re: find area under the curve using calculus

    Quote Originally Posted by HallsofIvy View Post
    There is no 'finding' (i- 1/n)\Delta x, that is an arbitrary choice. Once you have divided the interval 0 to 1 in n subintervals, each having length \Delta x, and so right endpoints \Delta x, 2\Delta x, 3\Delta x, ..., i\Delta x, ..., you must choose one x in each interval. Here they have just chosen the simplest- the midpoint: i\Delta x+ (1/2)\Delta x= (i+ 1/2)\Delta x. You could as easily have chosen (i+ 1/4)\Delta x or (i+ 1/3)\Delta x or (i+3/4)\Delta x, etc.

    In the last problem, all of the individual areas are rectangles or trapezoids. Do you know the formulas for area of a rectangle or trapezoid? Find the area of each and add them.
    hi
    thanks for your help HallsofIvy
    i will tray and solve as described
    thanks again
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  4. #4
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    Re: find area under the curve using calculus

    Basically just divide the region into a bunch of rectangles/trapezoids as HallsofIvy said. No calculus needed.

    However, if you want the exact area under the curve, say y = x^2, then you'd need an integral, \int_{0}^{1} x^2 \,dx, which is equal to 1/3.
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