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Estimate the area under the graph of f(x)= x^2 + 2 x from x=4 to x=10 using 3 approximating rectangles and left endpoints.

  • Calc -

    not clear what you mean by "left endpoints"
    I would mark off x= 4,6,8, and 10
    f(4), f(6), .. etc would give you the heights
    Do you want the rectangles to overlap or underlap?
    rectangle 1:
    larger =2 x f(6) = 2(48) = 96
    smaller = 2(f(4)) = 48
    difference = 48, which cut in half is 24
    so first rectangle estimation = 48+24 = 72
    do the same for the other two

    I got 128 and 200 for a total
    estimation of 400

    BTW, using integration gave me an exact area of 396

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