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The area under a curve

(1) If someone asks you for the rate under this curve over [a, b] then what region are they

asking you to find the area of? Shade it in.

ab

(2) Sketch the region underneath the curve y = x2/4 over [0, 4]. Estimate the area

underneath using the grid provided. (each small square is a 1 ? 1 square.)

(3) By breaking the interval [0, 4] at 1, 2, 3 draw four rectangles which overestimate the

area. Do so by maximizing f (x) = x2/4 over each small interval. To the right find

an underestimate by minimizing over each interval.

What is the total area of these rectangles?

(4) The result of the previous problem gives us an overestimate and an underestimate for

the area under the curve.

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