Math 22 The Area of a Region Bounded by Two Graphs

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Area of a Region Bounded by Two Graphs

Region 2 graph.png

 If  and  are continuous on  and  for all  in , 
 then the area of the region bounded by the graphs of  given by
 
 

Exercises

1) Find the area of the region bounded by the graph of and the graph of .

Solution:  
Find the bound of the region by setting , so , hence , then , therefore and
Check which function is the top function by choosing one number in between the bound and plug in:
Pick , so , and . Therefore, will be the top function.
Failed to parse (syntax error): {\displaystyle \text{Area}=\int_0^1 [f(x)-g(x)]dx=\int_0^1 [x^2-x^3]dx=[\frac{1}{3}x^3-\frac{1}{4}x^4]\Biggr_0^1=\frac{1}{3}(1)^3-\frac{1}{4}(1)^4=\frac{1}{12}}


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