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The area bounded by the curve $$y = \ln(x)$$ and the lines $$y = 0$$, $$y = \ln(3)$$ and $$x = 0$$ is equal to:
$$A = \int_{y_1}^{y_2} x \, dy$$
$$A = \int_{0}^{\ln(3)} e^y \, dy$$
$$A = [e^y]_{0}^{\ln(3)}$$
$$A = e^{\ln(3)} - e^0$$
$$A = 3 - 1$$
$$A = 2$$
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