Average value Definition and 107 Threads

Here is the problem: Find the average value of f\left(x, y\right) = x\;y for the quarter circle x^2 + y^2 \le 1 in the first quadrant. Here is what I have: Average value equation is \frac{1}{Area\;of\;R} \iint_{R} f\left(x, y\right) dA f\left(x, y\right) = x\;y =...

If the average salary S of an NBA player is increasing and can be modeled by: \frac{dS}{dt} = \frac{1137.7}{\sqrt{t}} + 521.3 and t = 5 is 1985. a. Find the salary function in terms of the year if the average salary in 1985 was $325,000. b. If the average salary continues to increase at...

I am in a time crunch and I am stumped... I need to find the average value function of f(x) = (3x+5)^2 on [1, 2] help please..

I am in a time crunch and I am stumped... I need to find the average value function of f(x) = (3x+5)^2 on [1, 2] help please..

Find the average value of \int_{x}^{1} cos(t^2)dt on [0,1] I have no idea where to even begin..

Hmmm... got this one wrong What is the average value of y = x^{2}\sqrt{x^3+1} on the interval [0,2] ? Okay, so another average value problem right? f(b) - f(a) = f'(c)(b-a) f(2) - f(0) = 2f'(c) 12 = 2f'(c) So then the average value is 6 right?

I forgot the formula for the average value of a function. Is that f(b) - f(a) = f'(c)(b-a) or am I thinking of something else?