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AP® Calculus AB-BC

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Moderate

Interpreting the Definite Integral

APCALC-J9NSSB

There are 120 letters in a mailbox at 12:00 pm. Over the next 5 hours, the number of letters in the mailbox changes at a rate modeled by the function $r(t)$, where $r(t)$ is integrable and measured in letters per hour, and $t$ is the time in hours since 12:00 pm. Of the following statements, which one is the best interpretation of $\int _{ 0 }^{ 3 }{ { r(t)dt } } $?

A

The rate at which the number of letters in the mailbox is changing, in letters per hour, at 3:00 pm.

B

The average rate of change in the number of letters in the mailbox between 12:00 pm and 3:00 pm.

C

The number of letters in the mailbox at 3:00 pm.

D

The change in the number of letters in the mailbox between 12:00 pm and 3:00 pm.