Download presentation
Presentation is loading. Please wait.
1
Area Under a Curve Riemann Sums
2
How do I find the area under a curve?
b
3
think rectangles! We can easily find the area of a rectangle, right?
Can I divide the area under my curve into rectangles?
4
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.
5
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.
6
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)
7
Let f(x) = x2 + 1 Draw rectangles from the right endpoint.
Compute area. This is called the Right Hand Sum (RHS)
8
Let f(x) = x2 + 1 Draw rectangles from the middle. Compute area.
This is called the Midpoint Sum
9
What did you find? Which area do you think is most exact?
Which is an under/over approximation? Why?
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.