F=xyi+yzj+zk. LetSbe the boundary of the cylinder 0≤z≤1,x2+y2≤1 (oriented outwards), andEthe interior. Compute∫∫S(F)·dSdirectly (S=S1+S2+S3, withS1=top,S3=bottom,S2=side. OnS1andS3you...

F=xyi+yzj+zk. LetSbe the boundary of the cylinder 0≤z≤1,x2+y2≤1 (oriented outwards), andEthe interior. Compute∫∫S(F)·dSdirectly (S=S1+S2+S3, withS1=top,S3=bottom,S2=side. OnS1andS3you can just say what dS is, but you must compute on S2.

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orchestra answered 2 years ago

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