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math_proof Group Title finding potential function for F=<-y,-x> is it just C? or is it -yx-xy+C? one year ago one year ago

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1. zepdrix Group Title

$\huge \vec{F}=-y\hat{i}-x\hat{j}$ $\large \vec{F}=M\hat{i}+N\hat{j}$$\large M=\frac{\partial f}{\partial x} \qquad N=\frac{\partial f}{\partial y}$We need to make sure that the second partials of M and N match,$\large M_y=-1 \qquad N_x=-1$Looks good. Soooo, hmm.. we'll integrate M with respect to x giving us, $\large -yx+g(y)$If we integrate N with respect to y we get, $\large −xy+h(x)$ So we need to look at each equation, see what part accounts for g(y) and h(x). Since -xy appears in both pieces, there is nothing else missing. The other term is simply a constant.$\huge f(x,y)=-xy+c$ I don't have the best understanding of this stuff quite yet, but hopefully that helps D: Lemme know if any of it is confusing.