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The graphs of two functions are shown with the areas of the regions between the curves indicated.

(a) What is the total area between the curves for $ 0 \le x \le 5 $?

(b) What is the value of $ \displaystyle \int_{0}^5 [f(x) - g(x)] dx $?

A) $39 .$ B) 15

Applications of Integration

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Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

the functions F N g r as shown. We want to determine what is the total area between the curves for his exit between zero and five. So we know that this first region has an area of 12 and the second region has an area of 27. So the total area total area is equal to 12 plus 27 which is equal to 39. Next, we want to determine the value of the integral of F minus g. So we see that in the first region F is below Gee So that means that this actually will be considered as a negative in the integral. And this area over here will be considered positive since F is greater than G. So the value of this integral is equal to here. We have a negative 12 plus a 27 which is equal to 15