Calculus Question

[PCMarine]

A quick AP calc question that I am reviewing has me puzzled; any ideas?

For a car traveling at a speed of s miles per hour, the fuel consumption of the car, C(s), is measured in gallons per mile. What are the units of Integral(b,a)[C(s) ds]?

A) Gallons
B) Hours per gallon
C) Gallons per hour
D) Miles per hour per gallon
E) Gallons per miles per hour


Thanks!

 

[Heisenberg]

Edit: Oops, missed that ds was miles per hour, not miles. So it'd be gallons per hour.

 

[Gibson486]

hint, you are integrating over b to a, which happens to be miles per hour....

 

[dullard]

Units of C(s): gallons/mile.

Units of ds (a small portion of s): mile/hour.

Units of C(s) * ds = (gallons/mile) * (mile/hour) = gallons/hour.

Integral is just adding a bunch of similar things together. 1 apple + 3 apples = 4 apples. The units don't change. Thus (C).

 

[Gibson486]

Originally posted by: Heisenberg
Edit: Oops, missed that ds was miles per hour, not miles. So it'd be gallons per hour.

you had me re reading the question and i thought i got it wrong for a sec too.....

 

[Heisenberg]

Originally posted by: Gibson486

Originally posted by: Heisenberg
Edit: Oops, missed that ds was miles per hour, not miles. So it'd be gallons per hour.

you had me re reading the question and i thought i got it wrong for a sec too.....

Heh, I'm so used to ds as an element of length that I just skipped over it.

 

[PCMarine]

Originally posted by: dullard
Units of C(s): gallons/mile.

Units of ds (a small portion of s): mile/hour.

Units of C(s) * ds = (gallons/mile) * (mile/hour) = gallons/hour.

Integral is just adding a bunch of similar things together. 1 apple + 3 apples = 4 apples. The units don't change. Thus (C).

hey thanks a lot guys, that actually makes a ton of sense.