Originally Posted by

**HallsofIvy** (a) Since the integrand is continuous for all t, the integral is defined for all x. I don't know what "and odd" means.

(b) Do you know the "fundamental theorem of Calculus"? I presume you mean "T'(x)", not "T(x)".

(c) Once you have found T'(x), T is "strictly increasing for all x", as long as T'(x)> 0. A function is convex if and only if its second derivative is positive, and concave if and only if its second derivative is negative. Its points of inflection are where the seocnd derivative is 0.

(d) The integrand is clearly less than [tex]\frac{1}{t^2}= t^{-2}[/itex]. So what can you say about the integral?