The area bounded by the curve y=(x) and the lines y=0, y=(c), x=0 is equal to:

Question

The area bounded by the curve $y=\ln(x)$ and the lines $y=0$, $y=\ln(c)$, $x=0$ is equal to:

Accepted Answer

*(Source uses a specific value $c=3$.)* $y=\ln x$ meets $y=\ln3$ at $x=3$.

$$\text{Area} = \int_0^3\ln(3)\,dx - \int_1^3\ln(x)\,dx = 3\ln3 - [x\ln x - x]_1^3 = 3\ln3 - (3\ln3-3+1) = 2$$

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