6.2 Area Between Curves - Area Between Curves Area between...

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Area Between Curves
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Area between curves Consider the region S bounded by the graphs of y = f ( x ), y = g ( x ) and the lines x = a and x = b . The graphs of f and g are continuous on [ a, b ]. ( ) ( ) f x g x Partition [ a , b ] into n subintervals of equal width and endpoints Create corresponding rectangles using, for instance, the left end points. x Area of S is roughly the sum of the areas of the rectangles: 1 0 ( ) ( ) Riemann Sum n i i i A f x g x x 0 1 2 , , , , n a x x x x b
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Area Between Curves NOTES: The graph of f must lie above the graph of g on the interval [ a, b ]. As n increases, the approximation becomes better and better, thus we can define the area of S as: 1 0 ( ) ( ) ( ) ( ) lim n b i i a n i A f x g x x f x g x dx 
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