Anonymous commented at 2008-12-22 04:26:03 » #24977

.................WUT?


2 Points Flag

Raep commented at 2008-12-22 09:13:05 » #24996

the area of the interval lies between the area of ([a->b] x [f(a)]) {meaning the red Box} and the area of ([a->b] x [F(b)] {being the green box}.

thus the area below f(x) = (the blue line) up to the x-axis, inbetween a and b is somewhere between the Area of the green and red box.

however, i would devide it into a few more intervals, to make it more accurate.

...

- oh yeah, btw, in the background there are two lesbian chicks having fun.

25 Points Flag

Anonymous commented at 2008-12-22 11:55:23 » #25006

I don't know who you are, Raep, but I love you.

14 Points Flag

Pergentile commented at 2009-12-24 17:43:18 » #184705

Seconded Anon 2

3 Points Flag

Anonymous commented at 2010-04-11 11:12:47 » #272790

this is how you keep you're students interested in math

5 Points Flag

Anonymous commented at 2010-05-23 05:26:11 » #309976

lol, squeeze theorem. So appropriate.

4 Points Flag

mathematician commented at 2013-07-09 02:17:42 » #1356319

This is not the squeeze theorem. Not even close. This is a consequence of the mean value theorem. For any function, the integral from a to b, then divided by (b-a) is the average value of the function on that interval. Thus, if f is strictly increasing, the average value of that function must be between the endpoints. The inequality is not strict if we have simple monotonicity.

7 Points Flag

mathematician commented at 2013-07-09 02:22:06 » #1356323

Must be between the function values of the endpoints* i meant to say. so f(a) < average value < f(b)

2 Points Flag