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# Calc for BusLife Sciences MATH 1314

UH

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This 6 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1314 at University of Houston taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/208412/math-1314-university-of-houston in Mathmatics at University of Houston.

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Date Created: 09/19/15

Math 13 14 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 each case total revenue is the area under the curve Agency A Agency B y y 1ooo 2ooo so 1ooo 2ooo 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 additional revenue that would be realized by using Agency B s ad campaign y 1ooo 2ooo 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 functiona x a Example 1 Find the area between the two curves v uswza v v 7x7 Example 2 Find the area between the function fx x3 4x and the x aXis from x 0 to x l Example 3 Find the area between the functions fx x2 9x and gx x Example 4 Find the area between the functions f x x3 and gx 2x and the veItical lines x 1 and x 1 Example 5 Find the area between the functions f x 6x and gx l and the x veItical lines x 3 and x 4 Example 6 Find the area completely enclosed by the functions f x J and gx x2 Example 7 Without any effort to curb population growth a government estimates that its population will grow at the rate of 458 02 thousand people per year However they believe that an education program will alter the growth rate to t2 45 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 8 A consumer magazine tested two kinds of engines One was a standard engine and it was determined that its acceleration could be modeled by f t 6 7t feet per secz t seconds after starting from rest The acceleration of the turbocharged model could be approximated by gt 6 16t05t2 feet per secz t seconds after starting from rest How much faster is the turbocharged model moving than the standard model at the end ofa 10 second trial 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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