Trapezoidal rule
This presentation is the property of its rightful owner.
Sponsored Links
1 / 12

Trapezoidal Rule PowerPoint PPT Presentation


  • 89 Views
  • Uploaded on
  • Presentation posted in: General

Trapezoidal Rule. Section 5.5. Recall, from Section 5.1…. All of our RAM techniques utilized rectangles t o approximate areas under curves. Another geometric shape may do this job m ore efficiently  Trapezoids!!!. Partition a function into n subintervals of equal length

Download Presentation

Trapezoidal Rule

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Trapezoidal rule

Trapezoidal Rule

Section 5.5


Trapezoidal rule

Recall, from Section 5.1…

All of our RAM techniques utilized rectangles

to approximate areas under curves.

Another geometric shape may do this job

more efficiently  Trapezoids!!!


Trapezoidal rule

Partition a function into n subintervals of equal length

h = (b – a)/n over the interval [a, b].

Approximate the area using the trapezoids:


Trapezoidal rule

Things to notice:

This technique is algebraically equivalent to finding the

numerical average of LRAM and RRAM!!!


Trapezoidal rule

The Trapezoidal Rule

To approximate , use

where [a, b] is partitioned into n subintervals of equal length

h = (b – a)/n.


Trapezoidal rule

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”:


Trapezoidal rule

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.


Trapezoidal rule

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???


Trapezoidal rule

Applying the Trapezoidal Rule

An observer measures the outside temperature every hour from

noon until midnight, recording the temperatures in the following

table.

Time

N

1

2

3

4

5

6

7

8

9

10

11

M

Temp

63

65

66

68

70

69

68

68

65

64

62

58

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:


Trapezoidal rule

Applying the Trapezoidal Rule

An observer measures the outside temperature every hour from

noon until midnight, recording the temperatures in the following

table.

Time

N

1

2

3

4

5

6

7

8

9

10

11

M

Temp

63

65

66

68

70

69

68

68

65

64

62

58

55

What was the average temperature for the 12-hour period?

We estimate the average temperature to be about 65 degrees.


Trapezoidal rule

Applying the Trapezoidal Rule

Let’s work through #8 on p.295…

(a) Estimate for volume using Trapezoidal Rule:


Trapezoidal rule

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.


  • Login