Download presentation

Presentation is loading. Please wait.

Published byCourtney Berkey Modified over 2 years ago

1
Section 5.5

2
All of our RAM techniques utilized rectangles to approximate areas under curves. Another geometric shape may do this job more efficiently Trapezoids!!!

3
Partition a function into n subintervals of equal length h = (b – a)/n over the interval [a, b]. Approximate the area using the trapezoids:

4
Things to notice: This technique is algebraically equivalent to finding the numerical average of LRAM and RRAM!!!

5
To approximate, use where [a, b] is partitioned into n subintervals of equal length h = (b – a)/n. The Trapezoidal Rule

6
Applying the Trapezoidal Rule Use the Trapezoidal Rule with n = 4 to estimate the given integral. Compare the estimate with the NINT value and with the exact value. Let’s start with a diagram… Now, find “h”:

7
Applying the Trapezoidal Rule Use the Trapezoidal Rule with n = 4 to estimate the given integral. Compare the estimate with the NINT value and with the exact value.

8
Applying the Trapezoidal Rule Use the Trapezoidal Rule with n = 4 to estimate the given integral. Compare the estimate with the NINT value and with the exact value. Do we expect this to be an overestimate or an underestimate? Why???

9
Applying the Trapezoidal Rule An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table. Time Temp N 63 1 65 2 66 3 68 4 70 5 69 6 68 7 8 65 9 64 10 62 11 58 M 55 What was the average temperature for the 12-hour period? But we don’t have a rule for f (x)!!! We can estimate the area using the TR:

10
Applying the Trapezoidal Rule An observer measures the outside temperature every hour from noon until midnight, recording the temperatures in the following table. Time Temp N 63 1 65 2 66 3 68 4 70 5 69 6 68 7 8 65 9 64 10 62 11 58 M 55 What was the average temperature for the 12-hour period? We estimate the average temperature to be about 65 degrees.

11
Applying the Trapezoidal Rule Let’s work through #8 on p.295… (a) Estimate for volume using Trapezoidal Rule:

12
Applying the Trapezoidal Rule Let’s work through #8 on p.295… (b) You plan to start with fish. You intend to have fish to be caught. Since, the town can sell at most 988 licenses.

Similar presentations

Presentation is loading. Please wait....

OK

Trapezoidal Rule Questions on HW

Trapezoidal Rule Questions on HW

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on porter's five forces model pdf Human brain anatomy and physiology ppt on cells Ppt on mission to mars Ppt on high level languages vs low level Ppt on australian continent highest Raster scan display ppt on tv Ppt on mammals and egg laying animals wikipedia Ppt on kisan call centre Ppt on hard gelatin capsule production Ppt on index numbers economics