Area Between Curves Problem

Question: To 2 decimal places what is the area enclosed between the curves:

When a=4.8 and b=12.5

Solution: We find the area beneath curves via integration (same as anti differentiation). So to find the area BETWEEN the curves we must find the area beneath the bigger one, and then subtract out the area that's beneath both of the curves.

So in the picture, the red and blue area is all of the area beneath the larger curve, but only the blue area is the are beneath the smaller curve. The red area is clearly the are between the curves. So we can think of the red area as the area underneath big curve MINUS the area beneath the small curve. Also, note that we're only considering the curves on the inter val [x1,x2], where these are the points of intersection of the two graphs. To find x1 and x2 explicitly, we set the equations equal to each other and find out what x has to be (since these x's are x1 and x2):

And so this gives us two x-values, namely:

These become the bounds of integration when we're subtraction the larger are from the smaller area, as explained above: