In a particular city, the amount of snow on the ground measured by the differentiable function f, where f(t) is measured in centimeters and t is measured in minutes after the beginning of a snow storm. What are the units of int_(2)^(10)f^(')(t)dt ? centimeters minutes centimeters / minute minutes / centimeter centimeters / minute ^(2) minutes / centimeter ^(2)

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In a particular city, the amount of snow on the ground measured by the differentiable function  f, where  f(t) is measured in centimeters and  t is measured in minutes after the beginning of a snow storm. What are the units of  int_(2)^(10)f^(')(t)dt ? centimeters minutes centimeters / minute minutes / centimeter centimeters / minute  ^(2) minutes / centimeter  ^(2)

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Rate of Change Interpretation: The integral of a rate of change (which is what f'(t) represents, as the derivative of f with respect to time) gives the net change over the interval. Since f(t) is measured in centimeters, and t is measured in minutes, the derivative f'(t) represents the rate of change of snow in centimeters per minute.Integration of Rate of Change: When we integrate f'(t) with respect to t over the interval from 2 to 10 minutes, we are essentially summing up the instantaneous rates of change (centimeters per minute) over the time interval (minutes). This will give us the total change in snow accumulation over that time period.Units of Integral: The units of the integral will be the product of the units of the derivative (centimeters per minute) and the units of the variable of integration (minutes). Multiplying these units together, the minutes will cancel out, leaving us with just centimeters.Conclusion: Therefore, the units of the integral ∫(from 2 to 10) f'(t) dt are centimeters.

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