Problem :
Find the total area between the graphs of f (x) = e^{x} and g(x) = 1 + 2x from x =  1 to
x = 1.
Note that
e^{x}≥1 + 2x on the interval
[ 1, 0] and
1 + 2x≥e^{x} on the interval
[0, 1]. Therefore the total area between the graphs is
 e^{x}  (1 + 2x) dx  =  (e^{x} 1  2x)dx + (1 + 2x  e^{x})dx 

 =  [e^{x}  x  x^{2}]_{1}^{0} + [x + x^{2}  e^{x}]_{0}^{1} 

 =  1  + [(2  e)  1] 

 =  
