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>> syms k a
>> f=sqrt(1-k^2*sin(a));
>> int(f,a,0,pi/2)
ans =
piecewise([k in Dom::ImageSet(x*1i, x, R_) & ~in(k^2, 'real'), 2*(k^2 + 1)^(1/2)*(ellipticE(2 - 2/(k^2 + 1)) - ellipticE(pi/4, 2 - 2/(k^2 + 1)))], [~k in Dom::ImageSet(x*1i, x, R_) | in(k^2, 'real'), int((1 - a*k^2)^(1/2)/(1 - a^2)^(1/2), a, 0, 1)])
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