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)^(10)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)^(10)f^(')(t)dt ? liters seconds liters / second seconds / liter liters  // second  ^(2) seconds / liter  ^(2)

Bytelearn · Accepted Answer

Rate of Change Integration: The integral of a rate of change gives the net change over the interval. In this case, f'(t) represents the rate of change of the water amount in the tank with respect to time. The integral of f'(t) from 3 to 10 seconds will give the net change in the amount of water over this time interval.Units of Integration: Since f'(t) is measured in liters per second (the rate at which the amount of water changes), integrating this rate over a time interval measured in seconds will give us the total change in liters. This is because when we integrate a rate (liters/second) over time (seconds), the units of seconds will cancel out, leaving us with just liters.Net Change Calculation: Therefore, the units of the integral from 3 to 10 of f'(t) dt are liters, which represents the net change in the amount of water in the tank between t = 3 seconds and t = 10 seconds.

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