Question

let f be a continious function on the closed interval [0,2]. If 2<(or equal to)f(x)<(or equal to)4, then the greatest possible value of (integral sign from 0 to 2) f(x)dx is?

Answer 1

the least it could be is
\[\int_0^22dx=2\times 2=4\]

Answer 2

how did you get that?

Answer 3

I don't know either hehehe

Answer 4

how did i get the integral?

Answer 5

more like where did the 2dx come from?

Answer 6

the least the function can be is 2, so i imagined it was always 2, i.e. it was \(f(x)=2\)

Answer 7

then the integral is base times height, i get \(2\times 2=4\) for the minimum possible value of the integral
if the function was always \(f(x)=4\) then \(2\times 4=8\) is the maximum

Answer 8

why is there a base times height thing?

Answer 9

oh I got it now.