If the area bounded by the curve \(e^{x^{2}}\), the \(x\)-axis, and the lines \(x=1\) and \(x=2\) is \(a\) sq units, what is the area bounded by the curve \(\sqrt{\ln(x)}\), the \(y\)-axis, and the lines \(y=e\), and \(y=e^4\).

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