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Viluxent Set 1 Paper 1 · Q10

Paper 1CalculusPowers & logarithmsNumber & counting

Let ⌊y⌋\lfloor y\rfloor denote the greatest integer less than or equal to yy. Find the value of

∫501/3log⁡5(⌊3x⌋⌊3x⌋+1) dx.\int_{50}^{1/3}\log_5\left(\frac{\lfloor3x\rfloor}{\lfloor3x\rfloor+1}\right)\,dx.
A−13log⁡5150-\frac13\log_5 150
B13log⁡5150\frac13\log_5 150
Clog⁡5150\log_5 150
D−log⁡5150-\log_5 150
E13log⁡550\frac13\log_5 50
F3log⁡51503\log_5 150

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