High School Calculus/Area Between Two Curves

Area Between Two CurvesEdit

The area between two curves can be more easily states as the area between two graphs.

In order to do this you must take the antiderivative of the two functions.

This is denoted by have a capital letter such as  

Let's take the graphs   and  

Let us also take the area between 2 and 4 as denoted by  

 

and

 

 

Now evaluate the antiderivatives from 2 to 4

 

 

 

 

Now we will evaluate the antiderivative G(x)

 

 

 

 

Now we take F(x)-G(x) to find the area between the two curves

 

 

Therefore,   between   and   is