Evaluate `int_(2)^(5)(x+[x])dx` ,where [.] denotes the greatest integer function.

Answer

C

Explanation

`x^(2)=16y`
The equation of tangent of P is

`x*4t=(16(y+t^(2)))/(2)`
`"or "4txx=8y+8t^(2)`
`"or "tx=2y+2t^(2)`
`A-=(2t,0), B-=(0,t^(2))` ltBrgt M(H,k) is the middle point of AB.
`h=t,k=-(t^(2))/(2)or2k-h^(2)`
Therefore, the locus of `M(h,k)` is `x^(2)+2y=0`.