Calculating Average Water Flow Rate with f(t) Function

[fiziksfun]

the rate at which water is sprayed is given by the function f(t)

during the time interval 0<t<4, what is the average rate of water flow??

I'm confused whether to use the formula

f(4)-f(0) / (4-0)

OR

$$\frac{1}{4}$$$$\int$$f(t) evaluated from 0 to 4.

help!

 

[tiny-tim]

Hi fiziksfun !

Hint: Suppose f(t) is a constant, C. Then f(4) = f(0) = C.

So which formula is right?

 

[fiziksfun]

i'm kind of slow, so i still don't understand :[
can you help me more??

 

[tiny-tim]

Sure!

If f(t) = C, a constant, then obviously the average of f(t) is C.

But f(4)-f(0) / (4-0) = (C - C)/4 = 0, which obviously is wrong.

And ∫f(t)/4 = ∫C/4 (evaluated from t = 0 to 4) = C, which equally obviously is right!

This works for any f(t), because f(t) is the rate of water, so ∫f(t) is the total water.

And so the average rate of water = total/time = ∫f(t)/4. ​

 

[fiziksfun]

ah, i think i understand, thank you!