Solve the problem.
-Find the area between y = ln x and the x-axis from x = 1 to x = 3.
A) $3 \ln 3 - 2$
B) $3 \ln 3 - 3$
C) $\ln 3$
D) $\frac { 2 } { 3 }$

Question

Solve the problem.
-Find the area between y = ln x and the x-axis from x = 1 to x = 3. 
A) $3 \ln 3 - 2$
B) $3 \ln 3 - 3$
C) $\ln 3$
D) $\frac { 2 } { 3 }$

Quizplus · Accepted Answer

The area under the curve $y = \ln x$ from $x = 1$ to $x = 3$ can be found by integrating the function with respect to $x$ over the given interval. The integral of $\ln x$ with respect to $x$ is $x\ln x - x$, and evaluating this from $x = 1$ to $x = 3$ gives $3\ln 3 - 3 - (1\ln 1 - 1) = 3\ln 3 - 2$, since $\ln 1 = 0$.

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