问题补充说明：图" class="ikqb_img_alink">
食势衡云测兰1
用参数程x=Rcost,y=Rsint,0<=t<=π
ds=√[x'(t)]^2+[y'(t)]^2=Rdt
(x+y)^3=2√2(R^3)[sin(t+π/4)]^3
原积=2√2(R^4)∫(0->π)[sin(t+π/4)]^3dt
=2√2(R^4)∫婷讨构位征字们括须掌(π/4->5π/4)(sinu)^3du
=2√2(R^4)∫(π/4->5π/4)[(cosu)^2-1]dcos照于诉起希胜脱则湖u
=2√2(R^4)[(cosu)^3/3-cosu]|(π/4->5π/4)
=10R物病杀业煤离^4/3
2
设P=cos(x+y^2)+2yQ=2ycos(x+y^2)+3x
所Q'x-P'y=1
设L1x轴(π,0)(0,0)段
L+L1段用格林公式,
∫(脸接见配两某预首口合L+L1)Pdx+Qdy=∫∫(Q'x-P'y)dxdy=∫∫dxdy=∫(0->π)dx∫(0->sinx)d欢y=2
且∫(L1)Pdx+Qdy=∫(π->0)cosxdx=0
所原积=∫(L)Pdx+Qdy=∫(L+L1)Pdx+Qdy360问答-∫(L1)Pdx+Qdy=2
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