# Applications of Integration

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These questions apply integration to concepts primarily in the physical sciences such as motion, flow, and work.

[Applications of integration] 1

Water is pouring out of a pipe at the rate of $f(t)$ gallons/minute. You collect the water that flows from the pipe between $t$ = 2 minutes and $t$ = 4 minutes. The amount of water you collect can be represented by:

A

$\int_2^4 f(t)dt$

B

$f$ (4) – $f$ (2)

C

(4 – 2) $f$ (4)

D

the average of $f$ (4) and $f$ (2) times the amount of time that elapsed

[Applications of integration] 2

If $f(t)$ is measured in gallons/minute and $t$ is measured in minutes, what are the units of $\int_2^4 f(t)dt$ ?

A

gallons/minute

B

gallons

C

minutes

D

gallons/minute/minute

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