Math Help - Find the numbers

1. Find the numbers

Let $\dpi{200} f(x) = \frac{\int_{0}^{\frac{\pi}{2}} t^x \cos{(t)} dt}{\int_{0}^{\frac{\pi}{2}} t^x \sin{(t)} dt}$

Fact: There exists unique real numbers r and c such that

$\dpi{200} \lim_{x \to \infty} \frac{f(x)}{x^r} = c$

Find the numbers r and c.

2. Re: Find the numbers

Where is Vlasev when you need him, lol.

3. Re: Find the numbers

quite complex