Calculus

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Estimate the area under the graph of 25−x 2 from x = 0 to x = 5 using 5 left rectangles.

b. Sketch for yourself the graph of f and the rectangles. Is this left sum an overestimate or underestimate? Enter OVER or UNDER.


c. Now use 5 right rectangles to estimate the area.


d. Is the right sum you got an overestimate or underestimate? Enter OVER or UNDER.

  • Calculus -

    y = 25 - x^2

    x _____ y

    0 _____ 25

    1 _____ 24

    2 _____ 21

    3 _____ 16

    4 _____ 11

    delta x = 1
    so
    25 + 24 + 21 +16 + 11 = 97

    b the rectangles are all ABOVE the curve, so the estimate is OVER

    c do it now with x = 1, 2, 3, 4, 5
    these rectangles are below the curve so under estimate

    real answer by the way:
    integral from x = 0 to x = 5 of 25-x^2

    25 x - (1/3)x^3 at 5 - at 0
    125 - (1/3)(125) = (2/3)(125) =83 1/3

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