Integrals · Question 9

JEE Main 2026 (Online) 4th April Morning ShiftMCQHard📈 Topic in 71% papers+4−1

Let -22 (| x|+[x x] )dx=2(3- 2)+ , where [ ] is the greatest integer function. Then ( 2 ) equals:

Answer

(2) 2

| x| and x x are even functions.

-22| x| dx=2 02 x dx=2(1- 2)

On [0, 2]: ddx(x x)= x+x x>0 (since x>-x there), so x x increases from 0 to 2 2 1.82.

Let x0 (0, 2) with x0 x0=1. Then [x x]=0 on [0, x0) and =1 on [x0, 2].

-22[x x] dx=2(2-x0)

Integral =2-2 2+4-2x0=2(3- 2)-2x0

=-2x0

2=(-2x0) (-x0)=2x0 x0=2

Answer: (2)

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