Question 17
Let $f: \mathbb{R} \rightarrow (0, \infty)$ be a continuous and periodic function. If $2$ is a period of $f$, show that:
a. $\int_{0}^{2} \frac{f(x+1)}{f(x)} \, \mathrm{d}x \geq 2$.
b. $\int_{0}^{2} \frac{f(x+1)}{f(x)} \, \mathrm{d}x = 2$ if and only if $1$ is a period of $f$.
a. $\int_{0}^{2} \frac{f(x+1)}{f(x)} \, \mathrm{d}x \geq 2$.
b. $\int_{0}^{2} \frac{f(x+1)}{f(x)} \, \mathrm{d}x = 2$ if and only if $1$ is a period of $f$.