Let [x] denote the greatest integer ≤ x. Consider the function f(x) = max x²,1 + [x]. Then the value of the integral ∫₀² f(x)dx is

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 29 Jan, Morning shift · Q2856

JEE Main 202329 Jan, Morning shiftMathematicsHardIntegral Calculus369× since 2002

Let

[x]

denote the greatest integer

\le x

. Consider the function

f(x) = \max \left\{ {{x^2},1 + [x]} \right\}

. Then the value of the integral

\int\limits_0^2 {f(x)dx}

JEE Main 2023 · 29 Jan, Morning shift · Q2856

JEE Main 202329 Jan, Morning shiftMathematicsHardIntegral Calculus369× since 2002

Let

[x]

denote the greatest integer

\le x

. Consider the function

f(x) = \max \left\{ {{x^2},1 + [x]} \right\}

. Then the value of the integral

\int\limits_0^2 {f(x)dx}