. Use a double integral to nd the volume of the solid bounded by the cylinder y2 + 2:2 = 2, and the planes 3: : 2y. :I: = U, z : 0 in the first octant. . Find the volume of the wedge cut from the elliptical cylinder 3:2 +9y2 = 25 by the planes 2 = [1' and z = 3.1: that is above the xy-plane lm where R is the solid bounded by the cone ya = 2:2 + 91:2 and the planes 5 = U. y = 9, y = 33: and :r = U. . Evaluate the integral . An elliptical lamina is bounded by the equation 1:2 f 4 + 3121/19 2 1. Its density is p{:::, y) = 3:2 gig. Find the mass of the lamina. Hint: You will need to use the formulas for sing?) and cos2 (9) twice. . Let F{;r:,y) = (yez, :1:ez._;ryez}. Show that F is conservative by nding its potential function._ and use it. to find de value of the line integral of F along any curve joining the point (1,110} to the point (3,1'J,1}. . Find the work done by the force field F = (, m) on a particle that moves along the path t} = (cos t, %sint). for U S t <_: :1:2de where s is the surface rr yg for d y l. . evaluate integral find flux of vector eld f="(0,01" along consisting on upper half sphere with radius use green theorem to compute line j: boundary square vertices l turn over sina ar v dy c circle centered at origen. area region enclosed by r t stokes curl x ye ze through part ellipsoid which lies above plane z="0." divergence volume solid parametriza g sin3 sin cos u and>