MathDB
2017 BMT Analysis #8

Source:

March 10, 2024
calculusintegrationfloor functionalgebra

Problem Statement

The numerical value of the following integral ∫01(−x2+x)2017⌊2017x⌋dx\int^1_0 (-x^2 + x)^{2017} \lfloor 2017x \rfloor dx can be expressed in the form am!2n!a\frac{m!^2}{ n!} where a is minimized. Find a+m+na + m + n. (Note ⌊x⌋\lfloor x\rfloor is the largest integer less than or equal to x.)
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