Answer
a) 39
b) 15
Work Step by Step
Part a)
This part is just asking for the total area of the region between f(x) and g(x), which we can find by adding the areas between the curves given in the problem image, which is just 12+27=39.
Part b)
This part asks for \int[f(x)-g(x)] over the interval from 0 to 5. By the definition of the area between curves, any area for this integral between the curves where f(x)>g(x) is positive and the area where g(x)>f(x) is negative.
With this in mind, we know that the area from 0 to 2 (12) is negative and the area from 2 to 5 (27) is positive. This means that the solution to the integral is 27+(-12)=15.
