Suppose represents flow rate of of cars driving through a given intersection every hour where represents midnight.

The definite integral represents...

Question

Suppose  represents flow rate of of cars driving through a given intersection every hour where  represents midnight.

The definite integral    represents...

BlackTom AI · Accepted Answer

The problem describes a flow rate function r(t), where t is measured in hours since midnight, and asks what the definite integral represents.

Since r(t) gives cars per hour, integrating r(t) over a time interval accumulates the total number of cars that pass during that interval. Therefore, the definite integral from a to b of r(t) dt represents the total number of cars passing through the intersection between times t = a and t = b.

In this specific context, 2am corresponds to t = 2 and 5am corresponds to t = 5. Thus, the integral from 2 to 5 of r(t) dt represents the total number of cars passing through the intersection between 2am and 5am.

Note on the provided data: the list of answer options is empty in the given input, so there are no alternative statements to evaluate. If options were present, we would compare them to the interpretation above and explain why the correct choice matches the idea that integrating a flow rate over an interval yields the total quantity (cars) over that interval, while incorrect options might misstate the interval, units, or the meaning of the integral (e.g., using a single time point, or summing rates without the interval).

MATH_1225_17243_202501 5.4 Indefinite Integrals and the Net Change Theorem

Suppose represents flow rate of of cars driving through a given intersection every hour where represents midnight. The definite integral represents...

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