The amount of water in a tank is measured by the differentiable function f, where f(t) is measured in liters and t is measured in seconds. What are the units of int_(0)^(10)f^(')(t)dt? liters seconds liters / second seconds / liter liters // second ^(2) seconds // liter ^(2)

Question

The amount of water in a tank is measured by the differentiable function  f, where  f(t) is measured in liters and  t is measured in seconds. What are the units of  int_(0)^(10)f^(')(t)dt? liters seconds liters / second seconds / liter liters  // second  ^(2) seconds  // liter  ^(2)

Bytelearn · Accepted Answer

Understand integral of derivative: Understand the integral of a derivative. The integral of the derivative of a function over an interval gives us the net change in the function over that interval. In this case, we are integrating the derivative of the water level function, f'(t), from t=0 to t=10 seconds. This will give us the net change in the water level over these 10 seconds.Determine units of integral: Determine the units of the integral. Since f(t) is measured in liters and t is measured in seconds, the derivative f'(t) will have units of liters per second (since it represents the rate of change of volume with respect to time). When we integrate f'(t) with respect to time, we are essentially summing up these rates over the interval from 0 to 10 seconds. The units of this integral will be the units of f'(t) multiplied by the units of t, which is seconds.Calculate units of integral: Calculate the units of the integral. The units of f'(t) are liters/second, and we are integrating with respect to time, which has units of seconds. Multiplying these units together (liters/second * seconds), the seconds cancel out, leaving us with just liters.

Full solution

More problems from Find derivatives of sine and cosine functions

Related topics