1. 3.8 Sum & Differences of Areas
Example: Find area enclosed between y=x2, y=(x–4)2 and the x-axis. y x 4  2
x2.dx
Area =
+ (x – 4)2.dx  2 4 2 = x3 3 2
(x – 4)3 3 + 2 4
Solve simultaneously
y = x2
( ) 8 3 =
( ) 3 -8 +
y = (x – 4)2
 x2 = (x – 4)2
= 5 units2 1 3
x2 = x2 - 8x + 16
0 = - 8x + 16
8x = 16
x = 2

2. 3.8 Sum & Differences of Areas
Example: Find area enclosed between y=x2 and y=x+2. y x -1 2
Area =
(x + 2).dx   -1 2
- x2.dx  -1 2
= (x x2).dx -1 2
Solve simultaneously x3 3 = -1 2 x2
+ 2x -
y = x2
y = x + 2
( ) =
2 + 4 – 8/3
( ) -
1/ /3
 x2 = x + 2
x2 - x – 2 = 0
= 4 1/2 units2
(x – 2)(x + 1) = 0
x = 2
x = -1