Calculus 3 :

final answers only are okay please highlight the final result !

Section 12.3: Problem 10 (1 point) For each of the following, set up the integral of an arbitrary function f(I, y) over the region in whichever of rectangular or polar coordinates is most appropriate. (Use t for $ in your expressions.) (a) The region -1.0 - With a = b = c=], and d = integral = It (b) The region 1 0 (1/sqpt(2),1/sqrt(2)) 1.0 With a = b = c= ], and d =[ integral = [Section 12.3: Problem 11 (1 point) Find the volume of the region between the graph of f(x, y) = 16-23 - y' and the cyplane. volume =Section 12.3: Problem 12 (1 point) Consider the solid shaped like an ice cream cone that is bounded by the functions z = vx2 + y? and z = v 18 - x2 - y?. Set up an integral in polar coordinates to find the volume of this ice cream cone. Instructions: Please enter the integrand in the first answer box, typing there for 8. Depending on the order of integration you choose, enter or and others in either order into the second and third answer boxes with only one or or dtheta in each box. Then, enter the limits of integration and evaluate the integral to find the volume. 1 1000 A = B = C = Volume =Section 12.3: Problem 13 (1 point) Match each double integral in polar with the graph of the region of integration. A B C ? ~ 4./ { { (7, 0 ) r de dr D D E F ? v 7. f (T , @ ) r de dr ? InTMOOUT G H No can earn 10% partial credit for 2 - 4 correct answers, 60% partial credit for 5- 6 correct answers, and 80% partial credit for 7 correct answers. Preview My Answers Submit AnswersSection 12.3: Problem 14 (1 point) Convert the integral below to polar coordinates and evaluate the integral. rydr dy Instructions: Please enter the integrand in the first answer box, typing theta for 0. Depending on the order of integration you choose, enter or and dtheta in either order into the second and third answer boxes with only one or or dtheta in each box. Then, enter the limits of integration and evaluate the integral to find the volume A = B = C = Volume = Note: You can earn partial credit on this problem. Preview My Answers Submit AnswersSection 12.3: Problem 15 (1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder c' + y" = 4 and bounded above by the plane > = I and below by the cy-plane. FIGURE 1 VSection 12.3: Problem 8 (1 point) For the region R below, write JUR f d.A as an iterated integral in polar coordinates. -5 5 -5 With a = b : C = and d = UnfdA = Safe fdA, where dA = Note: Use t for 0 in your expressions.Section 12.3: Problem 9 (1 point) (a) Graph r = 1/(5 cos @) for -7/2