MESA COLLEGE-SPR 2022 Math 252-83137 TR: 2:20-04 :15pm Rm MS-122 Inst: TRAN ALL WORK MUST BE SHOWN TO RECEIVE CREDITS. Real Test 4 (For Take-Home portion: Check answer -1pt) 1. Evaluate the double integrals: 3 y=-2x+6 TAKE HOME [1dydx b. Change the order of integration to dxdy, a . find new limits, set up integral, then x=0 >=0 evaluate. 2. Evaluate the double integral: y=2x TAKE HOME b. Change the order of integration to dxdy, a . find new limits, set up integral, then evaluate . V= 3. A region R is bounded inside a triangle with 3 vertices: A(0, 0) , B(3, 3) and C (5,0). The function is f(x, y) =x+2y. Find the double integral for f(x, y) over R a. using dydx TAKE HOME b. using dxdy 4. A region R is bounded inside the curve r = 4sin(0) , and outside the curve r=3. Find the area of the region using double integral a. using dr . do TAKE HOME b. using do. dr 5. Compute the volume of the solid that lies above the paraboloid z = x + y and below the sphere: x'+ y'+ z' = 1 a. using cylindrical coordinates TAKE HOME b. using rectangular coordinates 6. Find the volume of the region above the plane z=2 and below the sphere x ty + z = 9. a. using spherical coordinates TAKE HOME b. using cylindrical coordinates 7. Find the area of the surface f(x, y) = Vx2 + > over the triangle in the x-y plane formed by (0, 0), (2,0), and (0, 2). a. using rectangular coordinates b. using polar coordinates cylindrical : spherical: x = r . cos(@) y = r . sin(@) x = p. sin(p) . cos(0) y = p . sin(@) . sin(0) dV = r . dz . dr . do z = p. cos(p) r = p. sin(q) x2 + y2 + z? = p2 dv = psin($) . dp. do. de as = V1+ fx2 + fy2 . dA