Answer to Question #119355 in Calculus for Olivia

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