sparknotes
Applications of the Integral
Problems
Problem : Find the area of the region in the plane between the graphs of f (x) = | x| and g(x) = - x 2 + 6 .
(- x
2 + 6 - | x|)dx
(- x)dx - 
xdx
+ 6x
- 
|-2
0 - 
Problem : Find the total area between the graphs of f (x) = e x and g(x) = 1 + 2x from x = - 1 to x = 1 .
| e
x - (1 + 2x)| dx
(e
x -1 - 2x)dx + 
(1 + 2x - e
x)dx
1 - 
+ [(2 - e) - 1]
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