Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{π}{4}\)
A bowl is designed by revolving completely the area enclosed by y = x2 - 1, y = 3 and x ≥ 0 around the y-axis. What is the volume of this bowl?
If the volume of a hemisphere is increasing at a steady rate of 18π m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?
