*
1ã8ÏR^4/3
å©ç¨è½®æ¢ç§°æ§â«â«x^2dS=â«â«y^2dS=â«â«z^2dSæå积=2/3â«â« (x^2+y^2+z^2)dS=2/3â«â«R^2dS=2/3ÃR^2Ã4ÏR^2
2ã-zxi+yzj
å©ç¨æ度å
¬å¼æ度åé-zxi+yzj
3ã-ln(1-x)(-1ï¼xï¼1)
æ¶æåºé´(-1,1)设å½æ°s(x)é项æ±å¯¼ås'(x)=âx^(n-1)=1/(1-x)æå½æ°-ln(1-x)
4ãx^3+3x^2y^2+4y^3/3=C
å¾®ç¨å
¨å¾®ç¨å3x^2dx+6xy(ydx+xdy)+4y^2dy=0åd(x^3)+d(3x^2y^2)+d(4y^3/3)=0æx^3+3x^2y^2+4y^3/3=C
5ã[-1,0)
è®°t=2x+1å级æ°ât^2/n|u(n+1)/un|=n/(n+1)â1ææ¶æåå¾1|2x+1|ï¼1å³-1ï¼xï¼0级æ°ç»æ¶æx=0级æ°â1/nåæ£x=-1级æ°â(-1)^n/næ¶æææ¶æå[-1,0)
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