Directions: On all problems use fractions, not decimals. to find the exact answer in simplest form. You may use books, notes, a graphing calculator, a phone. You may not get any help from another person or a web site during the test. You must show your work [Show all the steps necessary to arrive at the solution.] to get credit. A correct answer with no work (or incorrect work) shown will receive no credit. 1) Use a double integral to find the area of the region enclosed by y= ixz and y = 2x. 2) Use polar coordinates to evaluate || j'R sin @dA with R being the region in the first quadrant outside the circle r= 2 and inside the cardioid r= 2 + 2 cos. 3) Find the surface area of the portion of the paraboloid z = x* + y* below the plane z = 1. 4) Use rectangular coordinates and a triple integral to find the volume of the solid region enclosed by z =5x% + 5y%and z = 6 7x* y2. Vox? J-'? xt-y? 5) Use cylindrical coordinates to evaluate f I x?dzdydx. Vgx2 fAw2 i 6) Use spherical coordinates to evaluate f jrv:i}_if O z2x% + y? + z2dzdydx