Recent content by yzc717

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    Finding the Center of Mass of D

    the problem is not given one. do I have to find the area of the two regions first? Then what do I do next?
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    Finding the Center of Mass of D

    Homework Statement Let D be the region in the (x, y) plane bounded by the lines y=x, y=4x and the hyperboals xy=1 and xy=9. find the center of mass of D. Homework Equations The Attempt at a Solution My thought: to use the center of mass formula? and use the change of variables?
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    Changing the Order of Integration for Double Integrals

    Homework Equations The Attempt at a Solution that is \int_0^{\sqrt{\pi}}\int_x^{\sqrt{\pi}} \sin(y^2) ~dy ~dx Reverse the order of the integrals (which is possible since the integrand is positive) : 0\leq x\leq y\leq \sqrt{\pi} \Rightarrow y ranges from 0 to \sqrt{\pi} 0\leq x\leq y\leq...
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    Question for final(vector field)

    [ My thought on problem#2: if f is scalar function, then this statement would be false?? Does this surface has to be a closed surface? My thought on problem #3: use Stoke's theorem? omega has to be no boundary? And I have no idea on the rest of it.