Using the substitutions $x = v$ and $y = \sqrt{u + v}$, evaluate the integral $\iint_{R} y \sin(y^2 - x) \, dA$ where $R$ is the region bounded by the lines $y = \sqrt{x}$, $x = 2$, and $y = 0$.
calculus-iiimultiple-integralschange-of-variablesjacobiandouble-integralintegration-techniquestrigonometric-integralsmultivariable-calculussubstitution-methodarea-elementcoordinate-transformationiterated-integrals
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