Consider [x] as the greatest integer function of x and {x}=x–[x].

Evaluate ∫{√x} dx for x=1 to 484.

NOTE: The greatest integer function is defined as a function that produces the "greatest integer less than or equal to the number" operated upon, symbol [x] or sometimes [[x]]. If the number is an integer, use that integer. If the number is not an integer, use the next smaller integer.

Changing the variable from sqrt(x) to u gives the equivalent integral of 2u{u} over [1,22], which can be written as the sum from K=1 to 21 of the integral of 2u(u-K) over [K,K+1], which evaluates to K+2/3, which sums to 11*21+14=245, confirming Eric's solution.

Edited on August 10, 2006, 3:07 pm

Posted by Richard on 2006-08-10 14:31:28