Unit of measurement for definite integral?

Cyrus T Buford

What is the unit of measurement for the above?

I can't find the answer anywhere

Michael Collins

What do you mean by unit of measurement?

Cyrus T Buford

That's what i don't understand.

The question is "What is the unit of measurement for...." and then the above picture is put in.


[Maybe part (a) of this particular question may be related to it, part (a) involved calculating the least squares regression line y=ax+b]

MathsManiac

The only reply I can think of that would make sense is to say that the unit of measurement for the integral is the product of the units of measurement on the x and y variables.

For instance, if this function was set in a context where x and y were both distances measured in cm, then the definite integral represents an area in square cm.

Cyrus T Buford

Thanks a million. That would make sense alright!
Thank You

Yakuza

Here's a concrete example:
Working the other way, starting with derivatives:
s = distance (measured in metres)
t = time (measured in seconds).
v = ds/dt = change in distance w.r.t. time (measured in metres / second).
a = dv/dt = change in velocity w.r.t. time (measured in meters / second²)

A typical integral involving velocity (w.r.t. time) where your velocity is a linear function of time is the function v = u+at
Integrating this function between 0 and time T will give you the area under the chart, the distance travelled in time T.
You are integrating velocity (measured in metres/second) w.r.t. to time (measured in seconds) giving you distance,
measured (as MM says) in units of metres/second * second or metres in its simplest form.