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.

Consumer Surplus and Producer Surplus

CS vs PS.png

 Given the demand function is  and the supply function is . 
 Let  be the solution of .
 
 Then, the Consumer Surplus is 
 
 and the Producer Surplus is 

Exercises

2) Find the consumer and producer surpluses by using the demand and supply functions .

Solution:  
Find the solution (equilibrium point): , so , so , then . Therefor, and
So
and

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