If ∫−13/2 |xsin⁡ πx|dx=k/π2, then the value of k is

I=∫−11 |xsin⁡πxdx|+∫13/2 |xsin⁡πx|dx=2∫01 xsin⁡πxdx−∫13/2 xsin⁡πxdx=2−xcos⁡πxπ+sin⁡πxπ201−-xcosπxπ+sinπxπ2=21π−−1π2−1π=3π+1π2,so⁡ k=3π+1.