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JEE Main20252 Apr 2025Morning ShiftMathematicsDefinite IntegrationActual

Let [.] denote the greatest integer function. If ₀^ e^3 [ 1 e ^ x -1 ] dx = - _ e 2 , then ^3 is equal to _______ .

Correct answer

0

Step-by-step solution

f(x)= 1 e^ x-1 =e^ 1-x array c|c f ( x )=2 & f ( x )=1 1 e ^ x -1 =2 & x =1 x =1- 2 & array f(0)=e^1=2.71 f (e^3 )=e^ 1-e^3 (0,1) I = ₀^ 1- n 2 2 dx + _ 1- n 2 ^1 1 dx + ₁^ e ^3 0 dx =2(1- n 2-0)+1(1-1+ 2)+0 - 2=2- 2 =2 ^3=8

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