Compute the average value 0fthe following function over the region R. 11: 11: f(x,y)=5cosxcosy R={(x,y): OSXSE' 053153} (Simplify your answer. Type an exact answer. using radicals as needed. Type your answer in factored form. Use integers 0r fractions for any numbers in the expression.) Evaluate the following integral. 5 (x + y) dA; R is the region bounded by y = - and y = - X R (x + y) dA = (Simplify your answer.) RCompute the curl of the following vector field. F = (3x2 - 5y2,5xy,z The curl of F is + K.Find the work required to move an object in the force field F = (x,3) along the straight line from A(0,0) to B(6,4). Check to see whether the force is conservative. Check to see whether the force is conservative. What is the potential function @? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The force is conservative, ((x, y) = (Type an exact answer.) O B. The force is not conservative, q(x, y) does not exist. Find the work. The work is (Type an exact answer.)Reverse the order of integration in the following integral. Ay 16- 16 Vy y = 4x f(x,y) dx dy 0 y/4 y = x x Choose the correct reversed integral below. O A. 16 4x O B. 4X 4 f( x,y) dy dx (x,y) dx dy 0 x 2 x2 0 O C. 4x 4 O D. 4 4x (x,y ) dy dx f (x,y) dy dx x2 0 0 2Evaluate the following line integral along the curve C. X ds, where C is the line segment from (1,1) to (35,35). xz + 12 The value of the integral is (Type an exact answer, using radicals as needed.)Z Find the mass of the solid cylinder D = {(r,6,z]: t] s r s 3. 0 5 Z S 4} with density p(r,6,z} = 1 + E. f ..... \\ Set up the triple integral using cylindrical coordinates that should be used to nd the mass of the solid cylinder as efciently as possible. Use increasing limits of integration. I I I[ dzdrde D The mass is . (Type an exact answer, using a: as needed.)