Is this right (integration problem)

[josephabney]

So my teacher asked us the question "If oil leaks from a tank at a rate of r(t) gallons/ minute at time t, what does the definite integral from 0 to 120 r(t)dt represent." Doesn't it represent the area of the tank from where t = 0 to where t = 120. Is that right?

 

[stapel]

So my teacher asked us the question "If oil leaks from a tank at a rate of r(t) gallons/ minute at time t, what does the definite integral from 0 to 120 r(t)dt represent." Doesn't it represent the area of the tank from where t = 0 to where t = 120. Is that right?

What do you mean by the "area" of the tank? Surface area? Or did you maybe mean "volume"?

You are given the rate of flow in gallons per minute. You are asked to integrate this rate from a beginning time to t = 120. Since t stands for "minutes", how much time is represented by t = 120?

If you integrate a rate of travel (a velocity, or linear distance per unit time), what do you get? You get the linear distance covered over the given time period.

If you integrate a rate of flow (volume per unit time), what do you get?

 

[Steven G]

So my teacher asked us the question "If oil leaks from a tank at a rate of r(t) gallons/ minute at time t, what does the definite integral from 0 to 120 r(t)dt represent." Doesn't it represent the area of the tank from where t = 0 to where t = 120. Is that right?

So the area of the tank is a function of time (minutes)? What do you even mean by area of tank? A tank is 3D and has volume or do you mean surface area?