解ï¼1ãåå¼=â«<1,2>y²dyâ«<y,1/y>dx/x² (ç»å¾åæï¼çº¦å»)
=â«<1,2>y²(y-1/y)dy
=â«<1,2>(y³-y)dy
=2^4/4-2²/2-1/4+1/2
=9/4ï¼
2ãåå¼=â«<1,2>x²dxâ«<1,x>ydy
=â«<1,2>x²(x²/2-1/2)dx
=1/2â«<1,2>(x^4-x²)dx
=(32/5-8/3-1/5+1/3)/2
=58/15ï¼
3ãåå¼=â«<-1,0>dxâ«<-x-1,1+x>(x²+y²)dy+â«<0,1>dxâ«<x-1,1-x>(x²+y²)dy
=2/3â«<-1,0>(4x³+6x²+3x+1)dx+2/3â«<0,1>(1-3x+6x²-4x³)dx
=2(1+2+3/2+1+1-3/2+2-1)/3
=4ã
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