Difference between revisions of "Math 22 The Area of a Region Bounded by Two Graphs"

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[[File:CS_vs_PS.png]]
 
[[File:CS_vs_PS.png]]
  
   Given the demand function is <math>d(x)</math> and the supply function is <math>s(x)</math>. Let <math>(x_0,p_0)</math> be the solution of <math>p(x)=g(x)</math>.
+
   Given the demand function is <math>d(x)</math> and the supply function is <math>s(x)</math>.  
 +
  Let <math>(x_0,p_0)</math> be the solution of <math>p(x)=g(x)</math>.
 
    
 
    
 
   Then, the Consumer Surplus is <math>CS=\int_0^{x_0} [d(x)-p_0]dx</math>
 
   Then, the Consumer Surplus is <math>CS=\int_0^{x_0} [d(x)-p_0]dx</math>

Revision as of 08:05, 17 August 2020

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 

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