Need Detailed Explanation Step by Step on paper

D Choose one of the below. An extra page has been left for workspace if you feel you need to use it. 40 pts 1) Find the volume of the region in space bounded by the below equations. You may use either a double or a triple integral. S z=0 z= f(x,y) = exty x =0 1 (x = Iny y =1 y = In 8) 2) Find the area of the region in the plane bounded by the below equations. You must use a double integral. (y =0 y=8 y=x3 ) 3) Find the volume of the solid region bounded above by the paraboloid given by z = f(x,y) = 9 - x2 - y? and below by the unit circle in the xy plane. You may use either a double or a triple integral. Hint: a change of coordinates would be helpful. Scanned with CamScanner E Choose one of the below. An extra page has been left for workspace if you feel you need to use it. 50 pts 1) Use a transformation (involving a Jacobian) to evaluate the below integral. Hint: the stuff under the radicals or in parentheses would be a great place to look for T-1. ('S Vxty (v-2x)? dy dx 2) Use cylindrical coordinates to evaluate the below. Where - S z S ; and the "shadow" of S in the xy plane is the unit circle. 3) Use spherical coordinates to find the volume of the solid region above the xy plane and between the sphere p = cos o and the hemisphere p = 2. Scanned with CamScanner Choose one of the below. An extra page has been left for workspace if you feel you need to use it. 20 pts 1) Reverse the order of integration of the double integral and evaluate. 2) Convert the below integral to cylindrical coordinates. You do not need to evaluate the integral. 3) Convert the below integral to spherical coordinates. Let S be the region bounded above by a hemisphere of radius 4 and below by the xy plane. You do not need to evaluate the integral. 4) Set up (but do not evaluate) your choice of a double or triple integral to find the volume of the region in the first octant beneath the plane given by 3x + y + 2z = 6