I've been trying to get knowledge with Riemann Steltjes integral and came across to some assignments in the web about the subject.In doing my practice I could´t achieve to the solution of a particular example that states as follows $$ \int_0^6 (x^2+[x])d(|3-x|) = $$ According to the assignment the solution is supposed to be 63.
I tried to get to the solution using two different ways but none solution coincide.
I developed the example like this $$ \int_0 ^3(x^2+[x])d(3-x) + \int_3^6 (x^2+[x])d(x-3) $$ which cancels the absolute value, and then $$ \int_0 ^3(x^2\cdot d(3-x)) +\int_0 ^3([x]\cdot d(3-x) +\int_3 ^6(x^2\cdot d(x-3) +\int_3 ^6([x]\cdot d(x-3)= $$ The problem is that I can't work out the integral that involves the$ [x]$ floor function. I searched your archives but couldn't get any hint. Doesn't seem that complicated but in fact I'stuck.
Can you give some help? Tks in advance