积ååºå被ç´çº¿ x+y=Ï/2 åå为两åï¼
D1ï¼0â¤yâ¤Ï/4ï¼yâ¤xâ¤Ï/2-yï¼
D2ï¼Ï/4â¤xâ¤Ï/2ï¼Ï/2-xâ¤yâ¤xï¼
å æ¤åå¼=
â«(0ï¼Ï/4)dyâ«(yï¼Ï/2-y) cos(x+y) dx
- â«(Ï/4ï¼Ï/2)dxâ«(Ï/2-xï¼x) cos(x+y) dy
=â«(0ï¼Ï/4) (1-cos2y) dy
-â«(Ï/4ï¼Ï/2) (cos2x-1) dx
=â«(0ï¼Ï/2) (1-cos2x) dx
=x - 1/2*sin2x | (0ï¼Ï/2)
=Ï/2 ã
çæ¡æ¯Ï/2-1
追çä¸è§å¾æ -1 åããã