Integrate the function f over the given region.
-$$f ( x , y ) = \frac { 1 } { \ln x } \text { over the region bounded by the } x \text {-axis, line } x = 5 \text {, and curve } y = \ln x$$
A) 6
B) 1
C) 4
D) 5

Question

Quizplus · Accepted Answer

We can set up the double integral as follows:
$$\int_{1}^{5}\int_{0}^{\ln x}\frac{1}{\ln x}dydx = \int_{1}^{5}\left[y\right]_{0}^{\ln x}dx = \int_{1}^{5}\ln x dx = \left[x\ln x - x\right]_{1}^{5} = 4$$
Therefore, the answer is Choice C.