(1 point) Consider the volume of the region shown below, which shows a hemisphere of radius 6 mm and a slice of the hemisphere with width Dy- Ay. D y Write a Riemann sum for the volume, using the sli...
Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly. Reimann sum Ay m3 definite integral dy - m3 5 m Ay 5 m 5 m Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly. Reimann sum Ay m3 definite integral dy - m3 5 m Ay 5 m 5 m
(1 point) Consider the area shown below. The curve drawn is x2 + y2 = 2, and we have used the notation Dy for Ay. (Click on the figure for a larger version.) Write a Riemann sum for the area, using the strip shown: Riemann sum= E Now write an integral that gives this area so where a = and b = Finally, calculate the exact area of the region, using your integral area =
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...