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How do I find the area under a function given the X and Y limits and equation?

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3 Answers

Find the domain of the composite function  f o g.
f(x)=           5               g(x)=     x + 5
             ---------- ,  
               x + 7

Since f(x) = 0, this is just the x axis, so this is the definite integral evaluated between the limits x = 2 and x = 10.


One of the best ways to approach this problem is a graphical approach: First plot the four lines ( y = x + 4, y=0, x = 2, and x = 10). You find that this encompasses a region that can be described as a combination of a rectangle and a triangle. From here you can use your knowledge of geometry to compute the area of each of these shapes and add them for the result.