JEE Main2014MathematicsDefinite IntegrationActual

If [ ] denotes the greatest integer function, then the integral ₀^ [ x d x is equal to:

Options

A2
B0
C-1
D- 2

Correct answer

D. - 2

Step-by-step solution

Let I = ₀^ [ x] d x I = ₀^ [ ( -x)] d x= ₀^ [- x] d x On adding (1) and (2), we get aligned &2 I = ₀^ [ x] d x+ ₀^ [- x] d x &2 I = ₀^ [ x]+[- x] d x &2 I &= ₀^ -1 d x ( [x]+[-x]=-1 if x Z) &2 I =- .x |₀ ^ =- & I = - 2 aligned

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