Area between two curves
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

Area Between Two Curves PowerPoint PPT Presentation


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

Area Between Two Curves. 7.1. Area Formula. If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the area of the region bounded above by y = f(x), below by y = g(x), on the left by x = a and on the right by x = b is…. .

Download Presentation

Area Between Two Curves

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


Area between two curves

Area Between Two Curves

7.1


Area formula

Area Formula

  • If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the area of the region bounded above by y = f(x), below by y = g(x), on the left by x = a and on the right by x = b is….


Area between two curves graph

Area between two curves (Graph)


Example 1

Example 1

  • Find the area of the region bounded above by y = x + 6 and below by y = x², and bounded on the sides by the lines x = 0 and x = 2.


Example 11

Example 1

  • Find the area of the region bounded above by y = x + 6 and below by y = x², and bounded on the sides by the lines x = 0 and x = 2.


Example 2

Example 2

  • Find the area of the region that is enclosed between the curves y = x² and y = x + 6


Example 21

Example 2

  • Find the area of the region that is enclosed between the curves y = x² and y = x + 6


Example 3

Example 3

  • Find the area enclosed by the curves

    and


Example 31

Example 3

  • Find the area enclosed by the curves

    and


Practice

Practice

  • Sketch the region enclosed by and then find the area.


Practice1

Practice

  • Sketch the region enclosed by and then find the area.


Example 4

Example 4

  • Find the area of the region that is enclosed between the curves x = y² and y = x – 2

  • What’s different about this question?


Example 41

Example 4

  • Find the area of the region that is enclosed between the curves x = y² and y = x – 2

  • What’s different about this question?


Two ways to solve

Two ways to solve…..

#1

  • Subdivide the regions

  • Equation of top graph – equation of bottom graph

  • Equations must be solved in terms of y and bound are determined by x values


Area between two curves

#2

  • Reverse the roles of x and y

    • When reversing roles you always subtract the graph on the right – graph on left

    • Must solve equations in terms of x and gets bounds in terms of y


Example 5

Example 5

  • Find the area of the region enclosed by the curves and x = 1.


Example 6

Example 6

  • Find the area of the region enclosed by the curves and


Practice2

Practice

  • Pg. 448 (1 – 23 odd)


  • Login