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Zach · Q2

CalculusNumber & counting

The symbol {x}\{x\} denotes the fractional part of xx. For example {10.4}=0.4\{10.4\}=0.4, {2}=0\{2\}=0. Given that f(x)=5x3+2x2+8x+1f(x)=5x^3+2x^2+8x+1, find

∫0nf({x}+1) dx\int_0^n f(\{x\}+1)\,dx

where nn is a positive integer.

A425n13\frac{425n}{13}
B12n(n+1)\frac12n(n+1)
C83n12\frac{83n}{12}
D437n12\frac{437n}{12}
E15n2+4n+815n^2+4n+8

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