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Note the last condition, or consider limit of Riemann sum $\Delta t=\frac{b-a}{n}$. As can be seen the expected integral should be positive: f[x_, y_] := x y/(1 + x + 2 y); p3 = Plot3D[f[x, y], {x, 0, 1}, {y, 0, 1}, MeshFunctions -> (#1^2 + #2^2 &), Mesh -> {{1}}, PlotStyle -> Opacity[0.5]]; pp = ParametricPlot3D[{t, Sqrt[1 - t^2], ...


Some time ago I developed a function for these sort of symbolic vector computations, called dotExand. For example, it will expand (2 x + 3 y, x-y) to 2(x,x)+(x,y)-3(y,y). Here I use the, at least in my country more common, notation (x,y) for the inner product of the vectors x and y. The advantage is that complicated expressions become more readable in this ...


Here is the best I've got so far. If you can be persuaded to write your vectors in a more distinguishable way, e.g. $v_1$ as v[1], then the following might work for you. I'm not so sure how robust it will be, but play around with it and let me know: Clear[specialDot] specialDot[expr_] := ReplaceAll[ Distribute[expr, Plus, Dot, Plus, Times], v[a_] v[b_] ...


I suspect you just need to do that yourself by defining your own div function div[{Power[r_,-2],0,0},{r_,_,_},"Spherical"]=DiracDelta[r]; div[args___]:=Div[args] div[{1/x^2,0,0},{x,y,z},"Spherical"] DiracDelta[x]

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