â«â«(D) Ïg(y+100)dsï¼å
¶ä¸D={(x,y)|x^2/0.04+y^2/0.09=1ï¼y>=0}
=â«(-0.2,0.2)dxâ«(0,â(0.09-9x^2/4))Ïg(y+100)dy
=Ïgâ«(-0.2,0.2)dx*(y^2/2+100y)|(0,â(0.09-9x^2/4))
=Ïgâ«(-0.2,0.2)[0.0045-9x^2/8+100â(0.09-9x^2/4)]dx
=Ïgâ«(0,0.2)[0.09-9x^2/4+300â(0.04-x^2)]dx
=Ïg*[0.09x-3x^3/4+6arcsin(x/0.2)+150x*â(0.04-x^2)]|(0,0.2)
=Ïg*(0.018-0.006+3Ï)
=Ïg*(0.012+3Ï)
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