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...

View Explanation

Log in for full answers

Similar Questions

Find the signed area produced by:[math: A=∫364cos(5x)dx](square units)Calculate your answer correct to 4 decimal places.(Note: Make sure your calculator is in radian mode.)

Find the area produced by:[math: A=∫16(8x3+12x2+4)dx](square units)

Evaluate the integral.

Evaluate the integral.

Graph the integrand and use geometry to evaluate the integral.

Find the area of the shaded region.

Graph the integrand and use geometry to evaluate the integral.

Solve the problem. Suppose that = 3. Find and .

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler