YES NOW I GOT IT!
[x*cos(x)-sin(x)]/[x^2] will be bigger than 0 because:
if 0<=x<=pi/2 then x<=tan(x) so x<=sin(x)/cos(x) xcos(x)<=sin(x) xcos(x)-sin(x)<=0
thus the derivative is negative or 0 on the interval
so sin(x)/x <= sin(pi/4)/(pi/4) because it is decreasing
so ∫(from pi/4 to...
Yes I tried that,
the derivative of the function sin(x)/x would be: [x*cos(x)-sin(x)]/[x^2]
the denominator will be bigger than 0. sin(x) is between 1/sqrt(2) and 1 cos(x) is between 0 and 1/sqrt(2). If I was sure that x is smaller that on or equal to one then I could conclude that the...
Homework Statement
∫(from pi/4 to pi/2)sin x/x ≤ 1/√2.
Homework Equations
The Attempt at a Solution
I know the pi/4≤x≤pi/2 and so 1/√2 ≤ sin x ≤ 1 and i have tried to manipulate this to no end and it has annoyed the living daylights out of me