Water flows from the bottom of a storage tank at a rate of
r(t) = 200 − 4t
liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 45 minutes.

Question

Water flows from the bottom of a storage tank at a rate of 
r(t) = 200 − 4t
 liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 45 minutes.

anonymous · Answer

$$\int\limits_{0}^{45} (200 - 4t) dt$$
sound right?

anonymous · Answer

yes

anonymous · Answer

is the antiderivative $$200t-2t^2$$

anonymous · Answer

Yes

anonymous · Answer

the answer is 4950

anonymous · Answer

Evaluate between 0 and 45
I get 9000 - 2(45^2)
Sounds right.

anonymous · Answer

The thing that's funny about these problems is that although the instantaneous rate is given as x liters/min, it never really flows for a whole minute at that rate, but changes constantly.  It's a little disconcerting.

anonymous · Answer

yeah thats what was confusing me thanks for the help

anonymous · Answer

yw