91Ó°ÊÓ

The current \(i\) in a certain circuit as a function of time \(t\) is given by the equation \(i=3 t^{2}+t .\) What is the total charge that passes a given point in the circuit in the first 2 s?

Find the coordinates of the centroid of the area bounded by the given curves. $$y=\sqrt{x}, x=0, y=2$$

Find the coordinates of the center of mass of the volume generated by rotating the area bounded by \(y=2 \sqrt{x}, y=0,\) and \(x=4\) about the \(x\) -axis.

Angular acceleration \(a\) for a rotating object is the time rate of change of angular velocity, \(\alpha=d \omega / d t\) (see Exercise 27 above). For \(\alpha=t^{2 / 3}\), find an expression for angular displacement \(\theta\) as a function of \(t,\) given that \(\theta=0\) and \(\omega=0\) when \(t=0\).