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MATHS HELP NEEDED: Imperial/Oxford MAT 2013 Paper

I don't understand the answer (or solution) to question 1) J) of the multiple choice of the 2013 Oxford/Imperial MAT paper. I'd upload a picture of the question and solution if I knew how...

Here's a link to the paper:
https://www.maths.ox.ac.uk/system/files/attachments/test13.pdf
(Page 7)

Here's a link to the solution:
https://www.maths.ox.ac.uk/system/files/attachments/websolutions13_0.pdf
(Bottom of page 3)
This is the Floor function. When 2x=5.52^{x}=5.5 the floor function would convert this to five. So for xx in range log25x<log26\log_{2}5\leq x<\log_{2}6 the floor function of 2x2^{x} will always give the integer 5. So for this we could consider the it to be a rectangle of height 5 and with width log26log25\log_{2}6-\log_{2}5 hence the area of this rectangle is 5(log26log25)5(\log_{2}6-\log_{2}5). By considering all of these rectangles added up you obtain the integral. Try look at the problem again with this in mind - you may have noticed it already though!
Original post by Cryptokyo
This is the Floor function. When 2x=5.52^{x}=5.5 the floor function would convert this to five. So for xx in range log25x<log26\log_{2}5\leq x<\log_{2}6 the floor function of 2x2^{x} will always give the integer 5. So for this we could consider the it to be a rectangle of height 5 and with width log26log25\log_{2}6-\log_{2}5 hence the area of this rectangle is 5(log26log25)5(\log_{2}6-\log_{2}5). By considering all of these rectangles added up you obtain the integral. Try look at the problem again with this in mind - you may have noticed it already though!

Thank you for this it makes sense now !

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