Let $$I = \mathop \smallint \nolimits_{x = 0}^1 \mathop \smallint \nolimits_{y = 0}^{{x^2}} x{y^2}dydx.$$ Then, I may also be expressed as

The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is

The solution of $$\frac{{{d^2}y}}{{d{t^2}}} - y = 1,$$ which additionally satisfies $${\left. y \right|_{t = 0}} = {\left. {\frac{{dy}}{{dt}}} \right|_{t = 0}} = 0$$ in the Laplace s-domain is

The equation of motion of a spring-mass-damper system is given by

$$\frac{{{d^2}x}}{{d{t^2}}} + 3\frac{{dx}}{{dt}} + 9x = 10\sin \left( {5t} \right)$$

The damping factor for the system is