Using the change of variable 2 = vandy = vu + v, set the integral SSR...
Calculate the integral using the type II method after the transformation: = SSR xy dA, where R is the region in the first quadrant bounded by the lines y = x, y = 3x, and the hyperbolas xy = 1, xy = 3. Make the transformation x = u/v and y = v
Change the tiple integral to spherical ordinate: $. «*+v++z33 av Where is bounded by the hemisphere 2 = 4-x2 - y2 and the xy - plane. 5." * S**** sing dpdepde s p sing dpdonde ["ST* pº sing dpdp.de "S" 5* p** sino dpdopde
2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis defined by z2 +--4for-1SS3,oriented away from y-axis. F-3 (b) Sis given by z2 + y2 + z2-9and F-1n+zk. (c) S is the conical face -V+ over the region r S 2 on the zy-plane, oriented downwards. 2. Flux calculations: Set up the double integral for Js F dA using cylindrical, spherical or shadow method as appropriate. (a) Sis...
set up iterated integrals for both orders of integration. then evaluate the double integral using the easier order and explain why it's easier. D y dA, D is bounded by y = x - 2, x=y2 (the D next to the double integral should be under the integral. I don't know how to put it in the right spot.
My professor said " Hint: Use change of variables formula u= xy, v= x^2 - y^2" 31. Consider the triple integral II w 2x dv, where W is the solid three-dimensional region bounded by the surfaces z = x2 + y2, z = 2(x2 + y2), and z = 1. Express it as an iterated integral in cylindrical coordinates. Do not evaluate it.
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)...
2. Set up and evaluate the volume integral for the region whose base D lies in the first quadrant in the xy plane and whose top is bounded by x + y + z = 4. 3. Find the volume that is enclosed by both the cone z = x2 + y2 and the sphere x2 + y2 + z = 2
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 integrationRin Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
Question 14 7 pts Consider the line integral F. dr where REC IND РІ. F(x, y, z) = i + (x+yz)j + (xy – z)k and C is the boundary of the plane 2 + y + z = 4 in the first octant, oriented in the counterclockwise direction when viewed from above. the following double integrals is equivalent to this line Using Stokes' Theorem, which integral? °6964 (3 - 2z+1) du dz (2x + y) dy da Question 12...
$*$*-* ? /12-** Rewrite the following integral using the order dydxdz (4 - x)/2 (12-3x -6y)/4 dzdydx 0 Select one: -S1*8*3 ayrics 5. $*$*2-43)* . ** -**-*/ Odydxdz c. None of the choices is correct answer (12-4z)/3 (12-3x - 4z)/6 d. dydxdz o PO 0 $* L*2-43/8/2-** 2z 2z e. dydxdz Set up a triple integral for the volume of the solid region bounded below by the paraboloid z = x2 + y2 and above by the sphere x2 +...