int0^2 x[2x]dx, where [.] denotes greate...

`int_0^2` x[2x]dx, where [.] denotes greatest integer function, equals : -

A

540

B

544

C

`17/4`

D

`33/44`

Verified by Experts

The correct Answer is:

C

`I=int_0^(1//2)0.dx+int_(1//2)^1 xdx+int_1^(3//2) 2xdx + int_(3//2)^(2)3xdx`
`=0+(x^2/2)_(1//2)+(x^2)_(1)^(3//2) + ((3x^2)/2)_(3//2)^(2) =17/4`

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