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JEE Main202529 Jan 2025Evening ShiftMathematicsDefinite IntegrationActual

If 24 ₀^ 4 ( |4 x- 12 |+[2 x] ) d x=2 + , where [ ] denotes the greatest integer function, then is equal to _______.

Correct answer

0

Step-by-step solution

Let I=24 ₀^ 2 ( |4 x- 2 |+[2 x] ) d x ...(i) Now |4 x- 12 |= cases -4 x+ 12 & ; x < 48 4 x- 12 & ; x 48 cases from ( i ) aligned & I=24 ₀^ 48 - (4 x- 12 ) d x+ _ 48 ^ 4 (4 x- 12 ) & + ₀^ 6 [2 x] d x+ _ 6 ^ 4 [2 x] d x & I=24 [ (1- 12 ) 4 - (- 12 -1 ) 4 )+ 4 - 6 & I=24 ( 1 2 )+ 4 - 6 & I=2 +12=2 + (from above) & =12 aligned

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