CHANGING THE ORDER of INTEGRATION V. Rewrite the double integral changing the order of integration. You must: Sketch a graph of the region of integration. Indicate the direction of the slices for the original integral in that graph. Label all curves and relevant values. Do the same thing for the new integral. HINT: You will need to use two double integrals for the region when you change the order of integration! 3 9+yz [ f(xy) dx dy 6y VI. Change the order of integration. Then evaluate the double integral. You must: Sketch a graph of the region of integration. Indicate the direction of the slices for the original integral in that graph. Label all curves and relevant values. Do the same thing for the new integral. (Note: You do get a nice number for the answer.) sec x tan x dx dy VIL. FINDING VOLUME USING DOUBLE INTEGRATION Find the volume of the region trapped inside the two surfaces where z = 0. Accurately sketch the two surfaces in IRS. Sketch the entire surfaces, not just the portion for which z 2 0. Write down the names of the surfaces. Sketch the 3-dimensional region whose volume you will find. Here you do use the fact that z = 0. Find C, the curve of intersection. Sketch the region D over which you will be integrating. Set up a valid double integral in rectangular coordinates that represents the volume. Convert the double integral to a double integral in polar coordinates. Do not evaluate the integrals. :) 3x2 + 3y2 + 23 = 9 and 1 = z? - x2 - y? where z 2 0. DOUBLE INTEGRALS IN POLAR COORDINATES VIII. Convert the double integral to polar form, then evaluate. Sketch the region R associated with the double integral ASUS