Spicy Limits and Integrals!
Calculus
Level
4
\[\begin{cases} \Omega_1 = \displaystyle \int_0^1 \sin^{-1} \left( \dfrac{x}{\sqrt{1+x^2}} \right) \mathrm{d}x \\ \Omega_2 = \displaystyle \int_0^1 \cos^{-1} \left( \dfrac{x}{\sqrt{1+x^2}} \right) \mathrm{d}x \\ \Omega_3 = \displaystyle \lim_{n \to \infty} \left( \dfrac{1}{n+1} + \dfrac{1}{n+2} + \ldots + \dfrac{1}{2n} \right) \end{cases} \]
Define \(\Omega_1, \Omega_2, \Omega_3\) as of above. Then which one of the following choices is correct?
by
Satyajit Mohanty