If M:SSxg dA , find R the (M) if R is the region bounded between the Line y = 3 and y = 2X-7 y = 1 1 and り- ら-2X and ご then reversed the Integration order of

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

A:

Q: Evaluate JJ, xy dA, where D is the region bounded by the curves xy = 2,4y = x² and y = 4. а.

A:

Q: Find [[fw ryz dV if W is the solid region in R³ below the surface z = x² + y² and above the square 0…

A:

Q: Evaluate 5² dV where E is the region below zx +2y + 4z = 8 in the first octant. Da B

A: Given problem:- Evaluate  ∫∫∫E  5x2dV where E is the region below x+2y+4z=8 in the first octant.

Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

Q: Evaluate J (2a² y +9y³)dA, D is the region bounded by y www 33522 a. 5 O b. 4811 5 OC. None of the…

A:

Q: Evaluate dA where R is the region given by 0sxs 1, 0s y s 1.

A: The question is taken from the calculus in which we have to find the double integral value  so We…

Q: Evaluate J, (2x + y) dV, where V is closed region bounded by the cylinder : = 4 – and the planes 4.…

A: Q. Evaluate ∭V(2x+y)dV, where V is closed region bounded by the cylinder z=4-x2 and the planes x=0,…

Q: Evaluate fSR f(x, y) dx dy, where R is the region given by 0<x < 2;0 < y < 5 and f(x, y) = 1 – ² –…

A:

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 10- 101 8- 8-…

A:

Q: Evaluate fSr f (x, y) dx dy, where R is the region given by 0< x< 2; 0 < y 5 5 and f(x, y) = 1 – –…

A:

Q: Consider the double integral (æ+1)² + (y – 1)² = 2 R R Where R is the region of Xy given Find the…

A:

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

A:

Q: Evaluate (2a² y +9y³)dA, D is the region bounded by y 33522 a. 5 Ob. 4811 5 C. None of the choices.…

A:

Q: Evaluate the moment M, and My of the region bounded by x = 2y – y² and the y=axis.

A:

Q: Use the change of variables s = xy, t = xy² to compute Sr xy² dA, where R is the region bounded by…

A:

Q: xy2 to compute fpxy2 dA, where R is the region bounded by ry 2, xy = 7, xy2 = 2, xy2 =7 Use the…

A: Given,

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: and above the region D in the ry-plane given by D = {(x, y) E R² | 0 < y < 1, y < z< Vy}.

A: Given  Surface : z=e5xx-x5 Region D=x,y∈R2| 0 &lt;y &lt; 1, y &lt;x &lt;y5

Q: Find the absolute maximum of f(z,y) = 4x – 2xy+ 6y-8z+ 2y+3 on the region R= {(x,y)|0 <AA2,-1 < y<…

A:

Q: (b) |(x+y)dA} where R is the region bounded by y=Jx and y = x² .

A:

Q: If M-SS xy dA , find the CM) if R is the region bounded betcween the R Line y = 3 and y= 1 and ら-2X…

A: Given :           M= ∬ xy dA   To find M if R is the region bounded between the line y = 1 and y =…

Q: Use Green's Theorem to evaluate F. ňds, where F = (Va+ 6y, 3z + 6y) C is the boundary of the region…

A: Solving this by green theoram

Q: Let f(x,y)=(x+y)² and D the region defined by D=((x,y); x² +y²sa?) then the double integral…

A:

Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: 3. Use the substititutions u = y – x, and v = y +2x to evaluate the integral (2x +y)(x – y) dx dy…

A:

Q: O Evaluate (9te"")dn + (ex+ Gary)dy where C is the boundary of the region enclared by 4x* and x=y?…

A:

Q: Evaluate x² + y2 dV _where E is the region that lies inside the cylinder E x2 + y? = 4 and between…

A:

Q: Evaluate (2a³y +9y³)dA, D is the region bounded by y 33522 a. 5 Ob. 4811 5 C. None of the choices.…

A:

Q: Q4 Calculate the integral Se²y-2x (y + 2x)³ da Where R is the region formed by joining the vertices…

A:

Q: Evaluate f S Sp(2+ e(=²+v²+z*)*/²) dV, where B = {(x, y, z) | x² + y² + z² < 9} Describe the region…

A: Consider the provided question, (2) (a)

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the %3D Vr2 + y? with…

A:

Q: F = (2x- 5e" + sin(z'), –4ry + In(r'), 5z - 3r°y) %3D across the boundary of the region W = {(r, y,…

A: Given F=2x2-5ey+sinz2,-4xy+lnx4,5z-3x2y6

Q: Given S J. 2. dy dx Rev erve the or der and ev aluate . Show Of Integration the region.

A:

Q: Sketch the region of integration and change the order of integration. So SN f(x, y)dyd.r f (x, y)…

A: The given integral is ∫04∫0xfx,ydydx. Use the limit values to identify the region of integration as…

Q: Q2. Let D = 2rza, + r cos² pa.. Evaluate (a) $, D. dS (b) S, V. Ddv over the region defined by 0 srs…

A: All are done in cylindrical coordinates

Q: Use Green's Theorem to evaluate nds, where F = (Va+ 6y, 3x + 6y) C is the boundary of the region…

A: Given that        F = &lt; √x + 6y , 3x + 6y &gt; C is the boundary of the region enclosed by y=x-x2…

Q: I V9+y? dy dæ by first interchanging the order of integration. Sketch the region of integration.…

A: Order of change of integrals

Q: c.) BRAW THE REGION OF INTEGRATION (ON RIGIHT) = ENDICATED 3Y Yxtave' dy dx アそ

A: “Since you have asked multiple questions, we will solve the one of the question for you. If you want…

Q: Verify that | (y -2x)dx + (2.xy + x² = [] dA where C is the boundary of a region R ây C R defined by…

A:

Q: : Evaluate ff,(x + 2y)dA, where D is the region in space bounded by y 2x and y = 1+ x2.

A: The given region D is bounded by the curvesy=2x2 and y=1+x2.We will find first the point of…

Q: 5. Evaluate z dV where E is the region bounded below by r2 +y² + z² = 4 and above %3D by r² + y² +…

A: We have to evaluate the integral ∭EzdV, where Eis the region bounded below by x2+y2+z2=4 and above…

Q: Evaluate J[(x+2y)dA, where D is the region bounded by the parabolas y=2x D and y=1+x².

A: Solution: Consider the given parabolas are y=2x2 and y = 1+x2 Draw the graph of the given curves and…

Q: If R is the region in the first quadrant bounded by x-axis, y = x 2 and 2x + y = 3, evaluate ZZ R x…

A:

Q: Use the change of variables x = u' - v², y= 2uw to evaluate the integral Sley dA, where Ris the…

A:

Q: By making an appropriate change of variables, evaluate the double integral I = (x + y)e²²-y², dædy…

A:

Q: Q1 Verify that [(v ²– 2x )dx +(2xy +x³\dy = | dA where C is the boundary of a region %3D дх ду R…

A: By  apply green theorem

Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…

Q: 36. Ifo = 45x y, evaluate ||] q o dV where V is the closed region bounded by the plane 4x +2y +z =…

A: The solution is given as

Q: Set up the triple integral 8y dV, where E is bounded by the coordinate planes and the plane x + y +…

A: To Set up the triple integral for 8y dV, where E is bounded by the coordinate planes and the plane x…