The rate at which the amount of water in a tank is changing can be measured by the differentiable function f, where f(t) is measured in liters per second and t is measured in seconds. What are the units of int_(3)^(5)f(t)dt ? liters seconds liters / second seconds / liter liters // second ^(2) seconds / liter ^(2)

Question

The rate at which the amount of water in a tank is changing can be measured by the differentiable function  f, where  f(t) is measured in liters per second and  t is measured in seconds. What are the units of  int_(3)^(5)f(t)dt ? liters seconds liters / second seconds / liter liters  // second  ^(2) seconds / liter  ^(2)

Bytelearn · Accepted Answer

Understand the integral: Understand the integral of a rate of change function. The integral of a rate of change function over an interval gives the net change in the quantity over that interval. Since f(t) represents the rate at which water is entering or leaving the tank in liters per second, the integral of f(t) from t=3 to t=5 will give the total amount of water that has entered or left the tank over those 2 seconds.Determine units: Determine the units of the integral. The function f(t) is given in liters per second, and the variable t is in seconds. When integrating with respect to t, the seconds in the denominator of the rate will cancel with the seconds from the dt term, leaving just liters as the unit for the integral.Conclude units: Conclude the units of the integral. Since the integral of a rate (liters/second) over time (seconds) results in a quantity (liters), the units of the integral ∫(3)^(5)f(t)dt are liters.

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