JEE Main202621 January 2026Morning ShiftMathematicsDefinite IntegrationActual

6 ₀^ |( 3 x+ 2 x+ x)| d x is equal to _ _ _ _ .

Correct answer

Step-by-step solution

Using 3x + x = 2 2x x : 3x + 2x + x = 2x(2 x + 1) = 2 x x(2 x + 1) Zeros in [0, ] : x = 0, /2, 2 /3, Expression is positive on (0, /2) , negative on ( /2, 2 /3) , positive on (2 /3, ) Let F(x) = - 3x 3 - 2x 2 - x F(0) = - 11 6 , F( /2) = 1 2 , F(2 /3) = 5 12 , F( ) = 5 6 ₀^ /2 = 7 3 , | _ /2 ^ 2 /3 | = 1 12 , _ 2 /3 ^ = 5 12 Total = 7 3 + 1 12 + 5 12 = 17 6 6 17 6 = 17

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