Answer:
1000 hours
Step-by-step explanation:
∫xf(x)dx = ∫x*xdx (1,0) + ∫x*(8-x)dx (2,1)
∫xf(x)dx = ∫x²dx (1,0) + ∫8x - x²dx (2,1)
∫xf(x)dx = ∫x²dx (1,0) + ∫8xdx (2,1) - ∫x²dx (2,1)
∫xf(x)dx = x³/3(1,0) + 8x²/2 (2,1) - x³/3(2,1)
∫xf(x)dx = 1/3 + 8(4/2 - 1/2) - (8/3 - 1/3)
∫xf(x)dx = 1/3 + 8(2-0.5) - (7/3)
∫xf(x)dx = 1/3 + 8(1.5) - 7/3
∫xf(x)dx = 1/3 + 12 - 7/3
∫xf(x)dx = - 6/3 + 12
∫xf(x)dx = - 2 + 12
∫xf(x)dx = 10
The average number of hours the family runs their vacuum cleaner in units of 100 hours
100 * 10 hours = 1000 hours
