Area between 2 curves:  Calc 2, Prof. G. Battaly, WCC

To find the area between 2 curves, we might like to start by finding the area below each of the 2 curves, and then subtracting. However, this only works if the area is found using definite integrals with the same upper and lower limits. So, start by finding the limits. Then proceed as below.  "If " is the integral of f(x) from x=0 to x= sqrt(2), "Ig" is the integral of g(x) from x=0 to x= sqrt(2),  and "Ih" is the integral of h(x) from x=0 to x= sqrt(2), where h(x) = g(x) - f(x)

Copy the url below.  Click on the Search symbol, then click on the folder.  Paste the url and enter.  If an id window pops up, enter battaly.com as the id name.  Skip the password.        

Direct Link:  http://www.battaly.com/calc/geogebra/area_2curves/area_2curves_start_f(x).ggb

The steps:      1.  Graph f(x)=x^2            2.  Graph g(x) = 4 - x^2           3.  Find the intersection of f and g.  
4.  Find Ig, the integral of g(x) from x=0 to x= sqrt(2)                             5.  Find If, the integral of f(x) from x=0 to x= sqrt(2)
6.  Graph h(x) = g(x) - f(x)                         7.  Find Ih, the integral of h(x) from x=0 to x= sqrt(2)
8.  Find Ig - If and compare to Ih.                                                                                        
Use the play and pause buttons to start the construction sequence to see these steps occur.

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