I think it diverges, but I must find whether or not.
. The problem is that they ask me to use a linear function lesser than the sine function over . I have no idea of how to start this.
Since for , the sine function is a concave function on this interval thus the line which passes through the points and is under the curve of . In other words, as long as .
If you don't know what a concave function is, you can show that is non negative on .
Hint : show that and that g is increasing on and decreasing on .
Note : choosing is useful (compulsory !) if one uses the fact that is a concave function. If one uses the second method, can be any real number which lies in .