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## Homework Statement

A fluid flows through a pipe. The flow varies with time. We want to estimate the volume of fluid (##V##, in ##L##) that passes through the pipe between time ##t = 10 s## and ##t = 14 s## (i.e. we want to integrate the flow between these times).

The available instrumentation allows us to measure the instantaneous flow rate (in ##L/s##) at any three times of our choosing. We might, for example, decide to measure the flow at ##t = 10 s##, ##t = 12 s##, and ##t = 14 s##. At what three times ##t_1, t_2, t_3## would you choose to measure the flow? Keep in mind that we want to produce the best possible estimate.

Now assume the results of the measurements are ##M(t_1)##, ##M(t_2)##, and ##M(t_3)## in ##L/s##. Give an expression for the volume of fluid that passes through the pipe in the period of interest.

## Homework Equations

## The Attempt at a Solution

So we want to estimate ##V = \int_{10}^{14} \text{flow}(t) \space dt##.

I think the times ##t_1, t_2, t_3## that have been mentioned in the problem are appropriate, but it obviously can't be that easy right? I can't really see how to break up the interval any better than that.

Then I would want to measure ##\frac{d \text{flow}}{dt}## at ##t_1, t_2, t_3## and call those ##M(t_1)##, ##M(t_2)##, and ##M(t_3)##.