Question

Let f(x,y)=y/x. Evaluating ∫f(x,y)dx


leads to



Select one:

a. −yln|x|)+g(x)

where g(x) is a function of x

.


b. yln|x|+g(y)

where g(y) is a function of y

.

c. ln(xy)



d. ln|y|+g(y)

where g(y) is a function of y

.

e. ln(xy)+g(y)

where g(y) is a function of y

.


f. ln(x)

Answer 1

By direct computations(see e.g., https://www.math.com/tables/integrals/tableof.htm), we get:

$\int f(x,y)dx=\int\frac{y}{x}dx=y\int\frac{1}{x}dx=y\,ln|x|+g(y)$

Answer: b). $y\,ln|x|+g(y)$