91Ó°ÊÓ

The voltage across a \(2.5-\mu \mathrm{F}\) capacitor in a copying machine is zero. What is the voltage after 12 ms if a current of 25 mA charges the capacitor?

Find the areas bounded by the indicated curves. $$y=x^{2}+2 x-8, y=x+4$$

Find the volume generated by revolving the regions bounded by the given curves about the \(y\)-axis. Use the indicated method in each case.$$y=8-x^{3}, x=0, y=0 \quad(shells)$$

A horizontal tank has vertical circular ends, each with a radius of \(4.00 \mathrm{ft} .\) It is filled to a depth of \(4.00 \mathrm{ft}\) with oil of density \(60.0 \mathrm{lb} / \mathrm{ft}^{3} .\) Find the force on one end of the tank.

The voltage across an 8.50 -nF capacitor in an \(\mathrm{FM}\) receiver circuit is zero. Find the voltage after \(2.00 \mu \mathrm{s}\) if a current (in \(\mathrm{mA}\) ) \(i=0.042 t\) charges the capacitor.

Find the coordinates of the centroids of the given figures. In Exercises \(11-22,\) each region is covered by a thin, flat plate. The solid generated by revolving the region bounded by \(y=x^{2}\) \(x=2,\) and the \(x\) -axis about the \(x\) -axis

The voltage across an 8.50 -nF capacitor in an FM receiver circuit is zero. Find the voltage after \(2.00 \mu\) s if a current (in \(\mathrm{mA}\) ) \(i=0.042 t\) charges the capacitor.

A swimming pool is \(6.00 \mathrm{m}\) wide and \(15.0 \mathrm{m}\) long. The bottom has a constant slope such that the water is \(1.00 \mathrm{m}\) deep at one end and \(2.00 \mathrm{m}\) deep at the other end. Find the force of the water on one of the sides of the pool.

Find the indicated volumes by integration. Describe a region that is revolved about the \(x\) -axis to generate a volume found by evaluating the integral \(\pi \int_{1}^{2} x^{3} d x\).

Find the coordinates of the centroids of the given figures. The solid generated by revolving the region bounded by \(y^{2}=4 x\) and \(x=1\) about the \(x\) -axis