原式=∫(0->兀/2)dx∫(0->x)cos(x+y)dy
=∫(0->兀/2)dx∫(0->x)cos(x+y)d(x+y)
=∫(0->兀/2)dx∫(0->x)dsin(x+y)
=∫(0->兀/2)dx *(sin2x-sinx)
=∫(0->兀/2)sin2xdx-∫(0->兀/2)sinxdx
=-1/2∫(0->兀/2)dcos2x +∫(0->兀/2)dcosx
=-1/2(cos兀-cos0)+(cos兀/2-cos0)
=-1/2(-1-1)+(0-1)
=1-1
=0
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