Definition (Definite Integral): Let be continuous on the closed interval

Some Quantity as an Accumulation Function:
If measures the amount of some quantity at time , then the Second FTIC says that the accumulated rate of change from time to is equal to the net change in that quantity over the interval

Exercise 3: Water leaks out of a 55-gallon tank at the rate where is measured in hours and in gallons. Initially, the tank is full.

1. 
   How much water leaks out of the tank between and hours?
   

2. 
   How long does it take until there are just 5 gallons remaining in the tank?
   

Exercise 4: Water leaks out of a 200-gallon tank at the rate where is measured in hours and in gallons. Initially, the tank is full.

1. 
   How much water leaks out of the tank between and hours?
   

2. 
   How long does it take until the tank is drained completely?