# Thread: application of integration to rate of flow

1. ## application of integration to rate of flow

Wine is leaking from a barrel at the rate of r(t) = 10 − 0.1t litres per minute.

i) If the barrel is empty after 100 minutes, how much wine did the barrel initially
hold?

ii) How much wine is in the barrel after 60 minutes?

I have never worked with flow before so just wanted to make sure what I was doing was correct.

I took the integral of the flow. Then put t = 100 in to find the c value. I found the value to be negative 500 so I think I did something wrong.

2. Originally Posted by stabza
Wine is leaking from a barrel at the rate of r(t) = 10 − 0.1t litres per minute.

i) If the barrel is empty after 100 minutes, how much wine did the barrel initially
hold?

ii) How much wine is in the barrel after 60 minutes?

I have never worked with flow before so just wanted to make sure what I was doing was correct.

I took the integral of the flow. Then put t = 100 in to find the c value. I found the value to be negative 500 so I think I did something wrong.

$\displaystyle \displaystyle \int_0^{100} r(t) \, dt$
amount left at 60 minutes = initial amount - $\displaystyle \displaystyle \int_0^{60} r(t) \, dt$