f g g g f f Name: ____________________________________________ Date: _________________ Period: __________ Section 7.1: Area of a Region Between Two Curves With a slight modification, we can change the concept of finding the area of a region under a curve to finding the area of a region between two curves. Consider the following graphs of () y fx and () y gx that are continuous on the interval 2,4 . 4 2 () () fx gx dx 4 2 () f x dx 4 2 () g x dx Example 1: Finding the Area of a Region Between Curves. Find the area of the region bounded by the graphs of 2 2, , 0 and 1. y x y x x x Sketch the graph and shade the region. x y Area of region between f and g Area of region under f = Area of region under g _ _ = Area of a Region Between Two Curves If f and g are continuous on [a, b] and () () gx fx for all x in [a, b], then the area of the region bounded by the graphs of f and g and the vertical lines x a and x b is () () b a A fx gx dx x y x y -1 1 2 3 -1 1 2 3 x y