= Solution
Integrating out the second coordinate gives the <probability density function> of the <marginal distribution>
$$
f_{X_1}(x)=\int_0^{\sqrt{h(x)}}\frac{2s}{H}\,ds=\frac{h(x)}H.
$$
Thus \b[the ratio has the normalized target <probability density function>]. The factor $s$ from the <Jacobian determinant> is essential; merely transforming the rectangular coordinates as if they remained uniform would give a different <probability density function>. This is the basis of the <ratio-of-uniforms method>.
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