Problem
Wednesday, Application March 19, 2008 7:15 PM
Two advertising agencies are competing for a major client. The rate of change of the clients revenues using Agency As ad campaign is approximated by f(x) below. The rate of change of the clients revenues using Agency Bs ad campaign is approximated by g(x) 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
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 Bs ad campaign.
We can compute the area between the two curves. The general formula is
a (top
b
function - bottom function) dx
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Examples 1 and 2
Wednesday, March 19, 2008 7:21 PM
1. Find area the between the two curves, f ( x ) = and g ( x ) = x 1 from x = 0 to x = 2.
1 2 x +2 5
2. Find the area between the function f ( x ) = x 3 x and the x axis from x = -1 to x = 1.
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Examples 3 and 4
Wednesday, March 19, 2008 7:24 PM
3. Find the area between the functions f ( x ) = x 2 4x and
g ( x ) = 4x .
4. Find the area between the functions f ( x ) = 3x 2 + 2 and
g ( x ) = x 3 , the vertical lines x = -1 and x = 3.
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Example 5
Wednesday, March 19, 2008 7:25 PM
5. Without any effort to curb population ...