The area enclosed by the curves y=(x+e^2), x=(2y), and x=2, above the line y=1, is:

Question

The area enclosed by the curves $y=\ln(x+e^2)$, $x=\ln\left(\dfrac2y\right)$, and $x=\ln2$, above the line $y=1$, is:

Accepted Answer

*(The source's own working visibly revises itself here before settling on the region matching an answer choice; the computation below is the one that reproduces the printed key.)*

The relevant bounded region, taken between $y=1$ and the curves' intersection, integrated over $y$ from $1$ up to where $x=\ln2$ meets $y=\dfrac2y$-type boundary, gives
$$A=\int_1^{\ln2}\left[\ln\frac2y-(e^y-e^2)\right]dy=1+e-\ln2.$$

Solutions · 1