The area of the region enclosed by the curves y=x, x=e, y=1x, and the positive x-axis is:

Question

The area of the region enclosed by the curves $y=x$, $x=e$, $y=\dfrac1x$, and the positive $x$-axis is:

Accepted Answer

$$\text{Area} = \int_0^1 x\,dx + \int_1^e\frac1x\,dx = \left[\frac{x^2}{2}\right]_0^1 + [\ln x]_1^e = \frac12+1 = \frac32$$

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