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# Class Note for MATH 1314 at UH

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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15

Math 1314 Lesson 21 Area Between Two Curves Two advertising agencies are competing for a major client The rate of change of the client s revenues using Agency A s ad campaign is approximated by fx below The rate of change of the client s revenues using Agency B s ad campaign is approximated by gx below In both cases x represents the amount spent on advertising in thousands of dollars In each case total revenue is the area under the curve given in thousands of dollars Agency A Agency B y y moo 2000 0 mac 2000 so This graph shows the relationship between the two revenue functions We see that one function is above the other The area between the two functions represents the projected additional revenue that would be realized by using Agency B s ad campaign Y 1000 2000 so This is an example of the kinds of problems you will be able to solve with the techniques you learn in this lesson We can compute the area between the two curves The general formula is 17 J top function bottom functiondx a Example 1 Find the area between the two curves fx xz 2 and gx x lfromx 0 tox 2 v msszz v v 7x7 5 4 3 Example 2 Find the area between the function fx x3 x and the x axis from x l to x l Example 3 Find the area between the functions f x x2 4x and gx 4x Example 4 Find the area between the functions f x 3x2 2 and gx x 3 and the veItical lines x 1 and x 3 Example 5 Without any effort to curb population growth a government estimates that its population will grow at the rate of 608 02 thousand people per year However they believe that an education program will alter the growth rate to t2 60 thousand people per year over the next 5 years How many fewer people would there be in the country if the education program is implemented and is successful Example 6 The management of a hotel chain expects its profits to grow at the rate of 2 l IE million dollars per year Iyears from now If the renovate some of their existing hotels and acquire some new ones their profits would grow at the rate of 1 24 4 million dollars per year Find the additional profits the company could expect over the next ten years if they proceed with their renovation and acquisition plans I ll use a graphing utility to generate the graphs of these two functions From this lesson you should be able to Find the area between two curves Sketch the graphs Set up the necessary integrals Find points of intersection if necessary Integrate and evaluate Solve word problems involving the area between two curves

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