Plotting a Density Function Defined in Terms of an Integral

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I want to plot the following function in 3D, but I first have to integrate w.r.t. y numerically since its not possible to get an analytical form.
a>0
Normally, I woulld just use
x_1 = linspace(-a,a,300);
x_2 = linspace(-a,a,300);
[X, Y] = meshgrid(x_1,x_1);
but the integral makes things a bit difficult. How can I work around this?

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