Calculus 3 :

Section 12.2: Problem 3 (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 y following iterated integrals. d- a) [/ f(z,3) dA = [ ]. f(z,y) dyda R AF -1 B= 3 -2 D= -5 -1 -2 1b) ([ f(z,y ) dA = [ [ f(x,y)didy -3 R -4 -2 -4 -3 -2 -1 G= H= -5Section 12.2: Problem 7 (1 point) V/9-y Consider the integral f(x, y) drdy. If we change the order of integration we obtain the sum of two integrals: f(x, y)dydr + f(x, y)dydr JA(z) le Jg(z) b = 91 (I)= 92 (I) = C = d = 93(I) : JA (I) =Section 12.2: Problem 9 (1 point) In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows: (, $(z,3) dA= [. J. (z,y)dedy + f(z,y)dady. Sketch the region D and express the double integral as an iterated integral with reversed order of integration. f(x, y) dyda 0 = b 91 (I) = 92 (I) =Section 12.2: Problem 11 (1 point) Consider the following integral. Sketch its region of integration in the xy-plane. 49 (" Le usin ( 27 ) dady (a) Which graph shows the region of integration in the xy-plane? |D 7 (b) Write the integral with the order of integration reversed: (." Se usin (2 ) da dy = ] [ usin(2 ) dy de A B with limits of integration 4 -49 A= B = 49 CE D = Vx (c) Evaluate the integral. 12 [e- 1] 49 C DSection 12.2: Problem 13 [1 point] Set up a double integral in rectangular coordinates for calculating the volume ofthe solid under the graph ofthe function x, 3;) = 22 7 22 7 f and above the plane :1 = . instructions: Please enter the integrand in the rst answer box. Depending on the order of integration you choose, enter air and dy in either order into the second and third answer boxes with only one air or dy in each box. Then, enter the limits of integration. Section 12.1: Problem 10 {1 point} Find The average value of ay) = Belly": + a! ever he rectangle R = [0,5] x [Ill| 6]. Average value = 59349 Section 12.1: Problem 11 {1 point] The table below gives values of z, }, the number ofmilligrams of mosquito larvae per square meter in a swamp. If m and yare in meters and R is the rectangle l] g :r: 3 ti, 0 g y g 12, estimate HR f{$,y)dA. In; re. Jam 53 (Include .u in your answer.) Hint Eva ate the Riemann sums using the lower left comers and upper right comers. Then take the average of the two Riemann sums. Section 12.1: Problem 12 (1 point) Calculate a Riemann sum $3,3 on the square R. = [0, 3] x [0, 3] for the function g(x, y) = f(x, y) + 9. The contour plot of f(c, y) is shown in Figure 4. Choose sample points and use the plot to find the values of f(x, y) at these points. Use the values of f(r, y) to evaluate g(x, y) accordingly. P11 P21 X 0 FIGURE 4 Contour plot of f(x, y). S3.3 103.5