I'm new to Mathematica, and trying to plot a function, but stuck at integrating the function for hours. What I want to do is to plotting the following function with respect to $x$. $$-\int^1_0\sum^n_{i=1}{n-1\choose i-1}^2(x-y)^2(xy)^{2i-2}(1-x^2)^{n-i}(1-y^2)^{n-i}2ydy$$ To do so, I defined a function $h$ which has 4 variable
h[x_, y_, i_, n_] = -(Binomial[n - 1, i - 1])^2*((x - y)^2)*(x y)^(2 i - 2) ((1 - x^2) (1 - y^2))^(n - i) 2 y
But I can't figure out how to make a summation over $i$ and then how to integrate with respect to $y$.
What should I do if I want to do the integration and summation of this multivariable function?
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. $\endgroup$ – b.gates.you.know.what Aug 28 '17 at 20:30