{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

calc notes lecture 29

# calc notes lecture 29 - = 2 4 Example 3 Determine the area...

This preview shows pages 1–7. Sign up to view the full content.

Lecture Section Objectives Assignment 30 5.5 The Area of a region Bounded by Two Graphs 5.5: 1-7 odd, 15-29 odd, 35, 37 , 51 Understanding Goals: 1. Understand how to find the areas of regions bounded by two graphs. 2. Understand how to solve real-life problems using the areas of regions bounded by two graphs. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Area between Curves Case I : The area between two continuous functions ( 29 ( 29 x g y x f y = = and on the interval [a, b] with ( 29 ( 29 x g x f [ ] ( ) ( ) b a A f x g x dx = - or ( 29 ( 29 [ upper function lower function ] , b a A dx a x b = - Case II: The area between two continuous functions ( 29 ( 29 y g x y f x = = and on the interval [c, d] with ( 29 ( 29 y g y f ( 29 ( 29 [ ] d c A f y g y dy = - or ( 29 ( 29 [ right function left function ] , d c A dy c y d = - * Note that if g f the area between f and g is ( 29 ( 29 b a f x g x dx - , regardless of the signs of f and g . 2
Example 1 : Find the area bounded by 2 , 2 1, 2, and the -axis. x y xe y x x y - = = + = 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example 2 : Determine the area of the region enclosed by ( 29 ( 29 x x g x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = , 2 4 Example 3 : Determine the area of the region bounded by 5 and 2 , 16 4 , 10 2 2 =-= + = + = x x x y x y 5 Sometimes it is easier to integrate with respect to y than with respect to x to find the area between two curves. Example 4 : Determine the area of the region bounded by ( 29 2 2 2 and 10-= +-= y x y x 6 Example 5 : An epidemic was spreading such that t weeks after its outbreak it had infected 2 1 ( ) 0.1 0.5 150 N t t t = + + , 0 50 t g people. Twenty-five weeks after the outbreak, a vaccine was developed and administered to the public. At that point, the number of people infected was governed by the model 2 2 ( ) 0.2 6 200 N t t t = -+ + . Approximate the number of people that the vaccine prevented from becoming ill during the epidemic. 7...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern