The number of people waiting in line to buy a new piece of technology is measured by the differentiable function f, where f(t) is measured in people and t is measured in hours after the store opened. What are the units of (1)/(2)int_(3)^(5)f(t)dt ? people hours people / hour hours / person people / hour ^(2) hours / person ^(2)

Question

The number of people waiting in line to buy a new piece of technology is measured by the differentiable function  f, where  f(t) is measured in people and  t is measured in hours after the store opened. What are the units of  (1)/(2)int_(3)^(5)f(t)dt ? people hours people / hour hours / person people / hour  ^(2) hours / person  ^(2)

Bytelearn · Accepted Answer

Understand Integral Units: Understand the integral and its units. The integral ∫_(3)^(5)f(t)dt represents the total number of people who have waited in line from hour 3 to hour 5 after the store opened. Since f(t) is measured in people and t is measured in hours, the integral itself has units of people multiplied by hours (people*hours).Consider Factor Effect: Consider the factor (1)/(2) and its effect on units. Multiplying the integral by (1)/(2) does not change the units. It simply halves the value of the integral. Therefore, the units remain people*hours.Determine Expression Units: Determine the units of the expression. Since the integral has units of people*hours, and we have not changed the units by multiplying by (1)/(2), the units of the entire expression (1)/(2)∫_(3)^(5)f(t)dt are still people*hours.

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