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[itex]\frac{1}{2} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(-|\xi|) 4 \phi_{\xi \eta} d \xi d \eta=0[/itex]

also apparently this is obvious after only doing the eta integral. any ideas why?

2, what is [itex]\nabla^2 f(x)[/itex] where [itex]f(x)=-|x|^2[/itex]

the answers say its -4

when i just do the second derivative with respect to x i get -2

and when i use index notation i get -6 since

[itex]\partial_i \partial_i r_j r_j = \partial_i (2 \delta_{ij} r_j)=2 \partial_i r_i = 2 \delta_{ii} =6[/itex]

what is going on here?