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Unit of measurement for definite integral?

  • 24-03-2019 4:02pm
    #1
    Cyrus T Buford
    Registered Users Posts: 45 ✭


    144-10.gif


    What is the unit of measurement for the above?

    I can't find the answer anywhere


Comments

  • #2
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,851 Mod ✭✭✭✭Michael Collins


    What do you mean by unit of measurement?


  • #3
    Cyrus T Buford
    Registered Users Posts: 45 ✭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]


  • #4
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭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.


  • #5
    Cyrus T Buford
    Registered Users Posts: 45 ✭Cyrus T Buford


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


  • #6
    Yakuza
    Registered Users, Registered Users 2 Posts: 5,141 ✭✭✭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.


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