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MATHS HELP NEEDED: Imperial/Oxford MAT 2013 Paper watch

    • Thread Starter

    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:
    (Page 7)

    Here's a link to the solution:
    (Bottom of page 3)

    This is the Floor function. When 2^{x}=5.5 the floor function would convert this to five. So for x in range \log_{2}5\leq x<\log_{2}6 the floor function of 2^{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 \log_{2}6-\log_{2}5 hence the area of this rectangle is 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!
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Updated: October 26, 2016
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