Evaluate the double integral l. dA, where Ris the region that x2 + y? lies between the circles x2 + y? = 9 and x + y? = 81, by changing to polar R coordinates. Answer: (1 point) For the integral 1xy dy dx, 9-x2 sketch the region of integration and evaluate the integral. Your sketch should be approximately the same as one of the graphs shown below; which is the correct region? Graph ? Then S", S"a-2 lxy dy dx Graphs: 1. 2. 3. -3 4. 5. 6. -3 (1 point) Calculate the double integral of f(x,y) over the triangle indicated in the following figure: f(x, y) = 14ye" 1 2 3 4 5 Answer : + 32 1 1 (1 point) If f(x) c dx = 5 and -3 | g(x) dx 3, what is the value of 3 /| f(xg(y) rectangle: dA where Dis the -3 < x < 1, 3 < y < 6? (1 point) Calculate the double integral S TR x cos(x + y) dA where R is the region: 0 < x (1 point) Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y? x + 6 and above the rectangle R = [-1,1] [1, 2]. - Answer: