(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]\displaystyle{r^{2}\int^{\arcsin\frac{r}{t}}_{0^{+}}\frac{\sqrt{2}\sin(\theta-\frac{\pi}{4})\sin(2\arcsin(\frac{t}{r}\sin\theta))}{1-\cos(2\theta)}d\theta + \int^{\arcsin\frac{r}{t}}_{0^{+}}\frac{\cos(\frac{\pi}{4}-\theta)}{1-\cos(2\theta)}d\theta - \int^{\arcsin\frac{r}{t}}_{0^{+}}\arcsin(\frac{t}{r}\sin\theta)d\theta + \int^{\arcsin\frac{r}{t}}_{0^{+}}d\theta}[/itex]

[itex] t = \sqrt{2}, r = 1[/itex]

This is once again beyond my skills for quite some time I imagine, but I am extremely curious to know the answer. The number empire integral calculator gives me that the second term approaches -∞ as theta approaches 0. Does this mean then that with 0+ I wind up with -∞ as the answer still? Or since the change in theta gets smaller too does it depend on the derivative? How do I find if there is a lower limit?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Another difficult integral/Also question on checking lower limit.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**