Net change (calculus)

Question

the amount of water in a tank is changing at the rate te^t gallons per day. what is the net change in volume in the tank between times. t=0 and t=1?

Answer 1

When we have a rate of change function, the net change on [a,b] is given by ∫_a^b f(t) dt.

Net change of volume = ∫₀¹ te^t dt = 1 gallon

The volume of water in the tank increases by 1 gallon in the first day.