CT8 April 2012 Q8 (iii) - Question 18 in revision notes

Can someone help me understand the how the differentiation is done?

 

An easier way to do this is to note that, if you have something like Integral{0,x} f(t)dt, this is just the integral of the function f(x). Eg, if f(t) = t^2, this would just be x^3/3. So, if you differentiate it, you'll just get back to the function f(x).

Here, Integral{K,Infinity} D0(a)da is the same as -Integral{Infinity,K} D0(a)da, and the letters are different. (We have K instead of x, a instead of t, D0 instead of f and Infinity instead of 0.) But, if you differentiate wrt K, you'll just get -D0(K), as before.

This was another very difficult question!