The value of is equal to where denotes the greatest integer function

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of ∫12(x⌊x2⌋+⌊x2⌋x) dx\int_{1}^{2} (x^{\lfloor x^2 \rfloor} + \lfloor x^2 \rfloor^x) \, dx is equal to where [⋅][\cdot] denotes the greatest integer function (1) 54+3+(23−22)+1log⁡3(9−33)\frac{5}{4} + \sqrt{3} + (2\sqrt{3} - 2\sqrt{2}) + \frac{1}{\log 3} (9 - 3\sqrt{3}) (2) 54+3+23+1log⁡2(23−22)+1log⁡3(9−33)\frac{5}{4} + \sqrt{3} + \frac{\sqrt{2}}{3} + \frac{1}{\log 2} (2\sqrt{3} - 2\sqrt{2}) + \frac{1}{\log 3} (9 - 3\sqrt{3}) (3) 54+23+1log⁡2(23−22)+1log⁡3(9−33)\frac{5}{4} + \frac{\sqrt{2}}{3} + \frac{1}{\log 2} (2\sqrt{3} - 2\sqrt{2}) + \frac{1}{\log 3} (9 - 3\sqrt{3}) (4) None of the above

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