Sketch the following region R. Then express S Sec.obda f(r,0)dA as an iterated integral over R....
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. Sketch the following region R. Then express Sfer f(r,0)dA as an iterated integral over R. R The region inside the lobe of the lemniscate ? = 6 sin 20 in the first quadrant. Sketch the region R. Choose the correct graph below. OA. OB. OC. OD AY 47 AY 47 4 4- 2 2- X X 0 Sketch the region and use integration to find its area. The region...
Thanks In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows: 0 f(x, y)dy dr f (r, y)dy d f(x, y) dA -2 2 TJ= Sketch the region and express the double integral integration as an iterated integral with reversed order of
Sketch the given region of integration and evaluate the integral over Rusing polar coordinates Sle**** da: R=(x? #y? 54% R Sketch the given region of integration R. Choose the correct graph below. OA OB Oc OD 55 - A- R (Type an exact answer
To evaluate the following integrals carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. х x,y): 0 5x57, 7 sys 6 - -x}; use x=7u, y = 6v - u. S5x25x+7y da,...
1) Given the following iterated integral. ex/Y DA R = y = 4x, y = -xy = 8 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (1.25 point) Evaluate the definite integral with the given function over the bounded region R.
(4pts) Sketch the region S in R over which the integral is computed. 3 T/2 3 2π 0 0 1 (4pts) Sketch the region S in R over which the integral is computed. 3 T/2 3 2π 0 0 1
Evaluate the given double integral by changing it to an iterated integral. xy dA; S is the triangular region with vertices (0,0), (10,0), and (0,7) O 35 12 0 1225 6 245 12 175 6
Write an iterated integral to evaluate the integral || 2?;} dA where R is the triangular region with vertices (18,0), (13,9) and (18,13). R Select all that apply -7 5 162 5 162 18 9 5 2+ - [ ] 22,3 dA= 5 22 43 dy do -7 + R 5 5 S] =2,3 dA – S139 -7 + 5 5 162 -2 + 5 5 22y3 dy do R 13 22,3 dA= -7 5 22 162 5 dy do...
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z. 1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte-gral which represents the volume of the ice cream cone bounded by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume =∫∫drdθ. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...