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Beyond Horizon Set 2 Paper 1 · Q7

Paper 1CalculusNumber & counting

For any real number xx, let ⌊x⌋\lfloor x\rfloor denote the greatest integer mm such that m≤xm\le x. Evaluate the following integral

∫−22⌊x2−1⌋ dx\int_{-2}^2\lfloor x^2-1\rfloor\,dx
A2(3−3−2)2(3-\sqrt3-\sqrt2)
B2(5−3−2)2(5-\sqrt3-\sqrt2)
C2(1−3−2)2(1-\sqrt3-\sqrt2)
D3(5−3−2)3(5-\sqrt3-\sqrt2)
E3(1−5−3)3(1-\sqrt5-\sqrt3)
FNone of the above

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