The area of the shaded part is ∫ 1? 1(tanπα4+ 1)dα-(4- 14？ π? 22)=4π? (-lncosπ4α+α)| 1？ 1-4+π=π-2,

The square has an area of 4,

∴ The probability that point P falls within the trademark area is equal to π? 24.

So choose: C.