Applications of Integration

 

 

 

Contents

  

Definite Integrals

  

Area Under a Curve

 

Area Bounded by 2 Curves

 

Volumes of Revolution

    

Quiz

  

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Area Bounded by 2 Curves

 
Say you have 2 curves y = f(x) and y = g(x)
 
 
 
Area under f(x)=
                              
Area under g(x)=
                              
 
Superimposing the two graphs,
 
Area bounded by f(x) and g(x)
                                                  
 
 
Find the area bounded by the curves y = x2 - 4x - 5 and y = x + 1
 
Solution:
 
Solving the equations simultaneously,
                              x + 1 = x2 - 4x - 5
                              x = -1 or x = 6
 
Sketch the graph:
                            
Required Area =