To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the...
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Transcript of To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the...
![Page 1: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/1.jpg)
To find the area under the curve
Warm-Up:Graph xxf 2
![Page 2: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/2.jpg)
Area under a curve for [0, 3] The area between the x-axis and the function
Warm-up
What is the area under the function on the interval [0, 3]?
![Page 3: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/3.jpg)
Find the area of the function from [0, 5]
![Page 4: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/4.jpg)
Find the area under the function
Problem???
![Page 5: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/5.jpg)
Riemann Sums Approximates the area under the curve using
rectangles Three different orientations for the rectangles
left
![Page 6: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/6.jpg)
Riemann Sums Approximates the area under the curve using
rectangles Three different orientations for the rectangles
left
middle
![Page 7: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/7.jpg)
Riemann Sums Approximates the area under the curve using
rectangles Three different orientations for the rectangles
left
middle
right
![Page 8: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/8.jpg)
Riemann Sums Sum the areas of all rectangle
-the height of each rectangle is f(x)-the width of each rectangle is dx
![Page 9: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/9.jpg)
Use Riemann sums to find the area under the curve
xf
![Page 10: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/10.jpg)
Left Riemann Sums Let dx = 0.5
![Page 11: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/11.jpg)
Left Riemann Sum
![Page 12: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/12.jpg)
Middle Riemann Sum
![Page 13: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/13.jpg)
Middle Riemann Sum
![Page 14: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/14.jpg)
Right Riemann Sums
![Page 15: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/15.jpg)
Right Riemann Sums
![Page 16: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/16.jpg)
Right vs Left Riemann Sums
![Page 17: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/17.jpg)
Determine the following Given a function, an interval and dx
Find:1. Sketch the function and the approximating rectangles using the midpoints2. Approximate the area under the curve
![Page 18: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/18.jpg)
On the interval [0, 4] 216 xxf dx = 1
1. Sketch
![Page 19: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/19.jpg)
2. Area
216 xxf
![Page 20: To find the area under the curve Warm-Up: Graph. Area under a curve for [0, 3] The area between the x-axis and the function Warm-up What is the area.](https://reader034.fdocuments.net/reader034/viewer/2022051306/5a4d1b8e7f8b9ab0599bfe65/html5/thumbnails/20.jpg)