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3Â¥: Originally posted by feixiaolin at 2014-01-05 18:25:41
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math2000: ½ð±Ò+20, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸, ·Ç³£¸Ðл 2014-01-05 20:15:54
Ϊ±ãÓÚÃèÊö£¬»ý·Ö±íʾΪIntegrate(Pdydz + Qdzdx + Rdxdy, S).
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P = tan[x^2/(1+|x|+|y|)] = tan[(1-z^2-y^2)/(1+|y|+sqrt(1-y^2-z^2)  )]ÊÇ y¡¢z µÄżº¯Êý¡£
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Ôò Integrate(Pdydz, S) = Integrate(Pdydz, Sh) + Integrate(Pdydz, Sb)
= Integrate(Pdydz, Dyz) - Integrate(Pdydz, Dyz) = 0.
ͬÀí¿ÉµÃ£¬Integrate(z^2sinx dzdx, S) = 0.
Integrate(Rdxdy, S) = Integrate((1-x^2-y^2)^1.5, Dxy)
= Integrate(da, 0, 2Pai) * Integrate( (1-r^2)^1.5 * r dr, 0, 1) (Áîu = r^2)
= Pai * Integrate( (1-u)^1.5, 0, 1) = 2Pai/5.
ËùÒÔIntegrate(Pdydz + Qdzdx + Rdxdy, S) = 2Pai/5.
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5Â¥2014-01-05 19:17:13
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