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MCQMediumJEE Main 2023 · 29 January, Shift 1Definite Integrals

Mathematics Question from JEE Main 2023 · 29 January, Shift 1

Let [x][x] denote the greatest integer ≤x\leq x. Consider the function f(x)=max⁡{x2, 1+[x]}f(x) = \max\{x^2,\, 1 + [x]\}. Then the value of the integral ∫02f(x) dx\int_0^2 f(x) \, dx is:

  • A

    5+423\frac{5 + 4\sqrt{2}}{3}

  • B

    8+423\frac{8 + 4\sqrt{2}}{3}

  • C

    1+523\frac{1 + 5\sqrt{2}}{3}

  • D

    4+523\frac{4 + 5\sqrt{2}}{3}

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