Question

Water is flowing into a tank at a rate of r(t)=t

2
ft
3
/min. How much water flows into the tank over the time interval 1 min. to 5 min.?

Answer 1

The exact amount of water that flows into the tank over the time interval 1 min. to 5 min. is 124/3 cubic feet.

Step-by-step explanation:

To find the amount of water that flows into the tank over the time interval 1 min. to 5 min., we need to integrate the rate of flow function r(t) with respect to time over this interval:

∫[1,5] r(t) dt = ∫[1,5] t^2 dt

Using the power rule of integration, we can integrate t^2 with respect to t:

∫[1,5] t^2 dt = [t^3/3] from 1 to 5 = (5^3/3) - (1^3/3) = 124/3

Therefore, the amount of water that flows into the tank over the time interval 1 min. to 5 min. is 124/3 cubic feet, or approximately 41.33 cubic feet.

Answer 2

The answer to your question is 15sq ft by 11