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.

This should be equivalent to the integral of sqrt(x)dx from 1 to 484 less the sum 1*3 + 2*5 + 3*7 + 4*9 + ... + 21*43.

The integral evaluates to (2/3)(484)^3/2 - (2/3)*(1)^3/2 = 7098 while the sum can be broken into the sum of 2n^2 and n from n=1 to 21 or 2(7*11*43) + (11*21) = 6853

The difference between the integral and the sum is:

7098 - 6853 = 245