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    Fundamental Theorem of Calculus.

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    Find area under the the graph f(x) =x between x=0 and x=1 by taking the limit of the sum of approximating rectangles whose heights are the values of the function at the right hand end point of each subinterval.

    © BrainMass Inc. brainmass.com December 24, 2021, 9:48 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/fundamental-theorem-calculus-414252

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    Find area under the graph f(x) =x between x=0 and x=1 by taking the limit of the sum of approximating rectangles whose heights are the values of the function at the right hand end point of each subinterval.
    Solution. Let f(x)=x. Let us equally partition the interval [0, 1 into n subintervals: [0, 1/n], [1/n, 2/n], [2/n, 3/n], ..., [(n-1)/n, 1], and ,
    Then we can take the right hand end point of each subinterval to form the following sum:

    So, the area is equal to

    Indeed, the area is equal to

    by the Fundamental Theorem of Calculus.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:48 pm ad1c9bdddf>
    https://brainmass.com/math/calculus-and-analysis/fundamental-theorem-calculus-414252

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