View by Category

Loading...

PPT – Area of a Region Between 2 Curves PowerPoint presentation | free to view

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Area of a Region Between 2 Curves

- Section 6.1

General Solution

- When determining the area between a function and

the x-axis - Graph the function first
- Note the zeros of the function
- Split the function into portions where f(x) gt 0

and f(x) lt 0 - Where f(x) lt 0, take absolute value of the

definite integral

Try This!

- Find the area between the function h(x)x2 x

6 and the x-axis - Note that we are not given the limits of

integration - We must determine zeros to find limits
- Also must take absolutevalue of the integral

sincespecified interval has f(x) lt 0

Area Between Two Curves

- Consider the region betweenf(x) x2 4 and

g(x) 8 2x2 - Must graph to determine limits
- Now consider function insideintegral
- Height of a slice is g(x) f(x)
- So the integral is

g

f

Area Between Curves

Find the area of the shaded region

Area Between Curves

Find the area of the shaded region

Area Between Curves

In general

Area Between Curves

In general

1. Find the area of the shaded region.

1. Find the area of the shaded region.

Find intersection points first.

2. Sketch the region represented by

2. Sketch the region represented by

top

bottom

- Representative rectangles are sometimes used.

A vertical rectangle (of width ) implies

integration with respect to x, whereas a

horizontal rectangle (of width ) implies

integration with respect to y.

- If 2 curves intersect at more that 2 points,

then to find the area of the region between the

curves, you must find all points of intersection

and check to see which curve is above the other

in each interval determined by these point.

In general, to determine the area between 2

curves, you can use

in variable x -vertical rectangles

in variable y - horizontal rectangles

Area Between Two Curves

- Sketch
- Determine which curve is on top
- Determine a and b
- Integrate!

Example

Find the area trapped between y x 2 and y 1.

y 1 y x 2

Top curve Bottom curve

Solve for a and b

x2 1, so x 1 and x 1.

The correct integral then is

Evaluate

Example

Set up an integral to find the area trapped

between y x and in the region for which x

is between 2 and 5.

Can we do this exactly

Example 6 Determine the area of the region

enclosed by

and .

The area is,

1. Find the area of the region bounded by

No calculator.

1. Find the area of the region bounded by

No calculator.

2. Use your calculator to find the area between

2. Use your calculator to find the area between

A

Intersection points

C

B

Store these values as the respective letter!

1. Find the area of the region bounded by

No calculator.

1. Find the area of the region bounded by

No calculator.

2. Find the area of the triangle with vertices

A(2,-3), B(4,6), and C(6,1).

2. Find the area of the triangle with vertices

A(2,-3), B(4,6), and C(6,1).

Integration as an Accumulation Process

- We can think of this as a function of b
- This gives us the accumulated area under the

curve on the interval 0, b

Try It Out

- Find the accumulation function for
- Evaluate
- F(0) 0
- F(4) 3
- F(6) 16

AP QUESTIONS

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

(No Transcript)

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

«

/ »

Promoted Presentations

Related Presentations

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2014 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2014 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Area of a Region Between 2 Curves" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!