Question

Average value of function

Answer 1

Average value of function f(x), in interval (a, b) :
\(\large \overline{y} = \frac{1}{b-a} \int \limits_a^b f(x) dx\)

Answer 2

Is this same as "y" coordinate of center of mass ?

Answer 3

whats the difference between "average value" and "y coordinate of center of mass" ?

Answer 4

one more question,
whats the difference between "average value" and "mean value"

Answer 5

just want to get the terminology straight

Answer 6

@whpalmer4 @Abhishek619

Answer 7

or anyone lol pls help :)

Answer 8

\(\large \overline{y} = \frac{1}{b-a} \int \limits_a^b f(x) dx\)
the hight of the the mean value rectangle
so the mean value thm , give u the existance
of mean value rectangle...
f'(c)=f(b)-f(a) /b-a
take the integral
\(\large f(c)= \frac{1}{b-a} (F(a)+(F(b))\)
\(\large f(c)= \frac{1}{b-a} \int \limits_a^b f(x) dx\)