The inequality holds on (pi/x, -pi/2). Use it to find a lower bound for the value of on the interval [0,1].
(I need LaTex help with putting the numbers up on the integral)
I have no idea how to do this.
What do they mean by lower bound? How do we find that with a inequality like this?
The answer is 7/6.
The fact that on (0,1) means, basically, that if we find , our answer will be less than on that same interval. Thinking about the integral as the area under the curve, if , then the area under sec(x) on (0,1) must be greater than or equal to the area under .
So to find the lower bound, we really need to evaluate:
, which gives
evaluated from 0 to 1, which gives your solution of .
Hope this helps!