Find the area enclosed by the given curves.
-Find the area between the curves y = ln x and y = ln 2x from x = 1 to x = 5.
A) ln 32
B) ln 16 - 8
C) ln 16
D) ln 2

Question

Quizplus · Accepted Answer

The area between the curves $y = \ln x$ and $y = \ln 2x$ from $x = 1$ to $x = 5$ can be found by integrating the difference of the two functions over the given interval. The difference between the functions is $\ln 2x - \ln x = \ln(2x/x) = \ln 2$. Thus, the area is given by the integral from 1 to 5 of $\ln 2$, which is $\ln 2 \times (5 - 1) = 4\ln 2 = \ln(2^4) = \ln 16$.

Find the Area Enclosed by the Given Curves