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

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 + 2 - x2).dx -1 2 Solve simultaneously x3 3 = -1 2 x2 + 2x - y = x2 y = x + 2 ( ) = 2 + 4 – 8/3 ( ) - 1/2 - 2 + 1/3  x2 = x + 2 x2 - x – 2 = 0 = 4 1/2 units2 (x – 2)(x + 1) = 0 x = 2 x = -1