Question

Calculus

A portion of the graphs of f(x), g(x), and the vertical line x = 1 are given below:

Moreover, we know that f and g are continuous for all x, and

\lim _{x \rightarrow \infty} f(x)=\infty, \lim _{x \rightarrow \infty} g(x)=3, \lim _{x \rightarrow-\infty} f(x)=0, \lim _{x \rightarrow-\infty} g(x)=3

What is the area of the region bounded by these three curves?

\int_{1}^{3}(g(x)-f(x)) d x

\int_{-\infty}^{1}(f(x)-g(x)) d x+\int_{1}^{4}(g(x)-f(x)) d x

\int_{-\infty}^{1}(f(x)-g(x)) d x

\int_{1}^{4}(g(x)-f(x)) d x

\int_{1}^{4}(f(x)-g(x)) d x