i need some help or understanding or a book or material that explains this type of problem

find the value of

thanks

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- Jun 29th 2013, 02:23 AMlawochekelintegration theorem!
i need some help or understanding or a book or material that explains this type of problem

find the value of

thanks - Jun 29th 2013, 06:29 AMHallsofIvyRe: integration theorem!
That is an example of a "Stieljes" integral. The original "Riemann" integral, , divides the x-axis into sub-intervals, , and then measures the "area" by where is just the length, . The "Stieljes" integral, , generalizes that by measuring each sub-interval by where can be any increasing function of x. If happens to be

**differentiable**the Stieljes integral reduces to a Riemann integral: .

But does not have to be differentiable or even continuous. One application of the the Stieljes integral is to be able to write a sum as an integral: if then is non-zero only for and to be on different sides of an integer: .

That, together with the fact that

should be enough for you to do this problem.

(By the way, I have interpreted your "[x]" as the floor function. Latex has "lfloor" and "rfloor" to get . - Jun 29th 2013, 07:06 AMlawochekelRe: integration theorem!
do u carry out normal integration on

thanks - Jun 29th 2013, 08:52 AMHallsofIvyRe: integration theorem!
Yes, of course.