Calculus 3 :

final answers only are okay please highlight the final result !

Section 12.2: Problem 10 (1 point) Evaluate the integral by reversing the order of integration. dxdy =Section 12.2: Problem 11 (1 point) Consider the following integral. Sketch its region of integration in the xy-plane. y 49 Jo Sip usin ( 2 ) dady (a) Which graph shows the region of integration in the xy-plane? ? v (b) Write the integral with the order of integration reversed: A B (" Se usin( 2 ) dady = [ ysia(2 ) dud 19 A B with limits of integration y y -49 A= B = CE D = (c) Evaluate the integral 49 C DSection 12.2: Problem 12 (1 point) Consider the following integral. Sketch its region of integration in the xy-plane. ly 3 3ry dy dx 16 1' 1 (a) Which graph shows the region of integration in the xy-plane? ? v -2 (b) Evaluate the integral. -2 -9 -2 2 A B 3 - 2 -2 -9 -2 -1 2 -3 -2 C DSection 12.2: Problem 13 (1 point) Set up a double integral in rectangular coordinates for calculating the volume of the solid under the graph of the function f(x, y) = 22 - x2 - y' and above the plane z = 6. Instructions: Please enter the integrand in the first answer box. Depending on the order of integration you choose, enter dx and dy in either order into the second and third answer boxes with only one x or dy in each box. Then, enter the limits of integration. A = B = C = D =Section 12.2: Problem 14 (1 point) Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the limits of integration for the following iterated integrals. ta) / / f(zu) da - [ J. f(z,y) du da R A= B= -1 (b) [/ f(z, ) da = [ ] f(z,y) dady -2 R -3 -4 -3 -2 -1 2 3Section 12.2: Problem 15 (1 point) Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R. Find the limits of integration for the following iterated integral. (a) f(z, y) dA = f(z, y) dy da R A= 1 -1 -2 -3 -4 -4 -3 -2 -1 1 3Section 12.2: Problem 16 [1 point} Consider the following integral. Sketch its region of integration in the torplane. a, z [Ufa lntz) my (3) Which graph shows the region of integration in the xyplane? ? v ([1) Write the integral with the order of integration reversed: ff: 111:2) my 2 LEE 111:2) M\" with limits of integraljon (c) Evaluate the integral. C] Section 12.2: Problem 17 {1 point} Find the volume of the region under the graph of u}, y} = 5:: + y + 1 and above the region g2 g m, [i g z 1': 9. VOIUIT'IE = C]