Area Under a Curve Riemann Sums.

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Presentation transcript:

Area Under a Curve Riemann Sums

How do I find the area under a curve? b

think rectangles! We can easily find the area of a rectangle, right? Can I divide the area under my curve into rectangles?

Start easy… Draw rectangles from the left endpoint. b Draw rectangles from the left endpoint. Draw rectangles from the right endpoint. Draw rectangles from the middle.

Let f(x) = x2 + 1 from [0, 2], n = 4 Let’s approximate the area under the curve. Graph it! a = 0, b = 2 : [0, 2] n = 4 (n = # of rectangles) Divide your interval into 4 rectangles.

Let f(x) = x2 + 1 Draw rectangles from the left endpoint. Compute area. Area ~ A1 + A2 + A3 + A4 The is called the Left Hand Sum (LHS)

Let f(x) = x2 + 1 Draw rectangles from the right endpoint. Compute area. This is called the Right Hand Sum (RHS)

Let f(x) = x2 + 1 Draw rectangles from the middle. Compute area. This is called the Midpoint Sum

What did you find? Which area do you think is most exact? Which is an under/over approximation? Why?