6. Below is the solid bounded by the surfaces S1:z° = 16 – 2y S2: x = 4-y + z, S3: x = 1, in the first octant La proyección del sólido en el plano XY corresponde a:

Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

Q: Calculate F· dS where F = (3xy', ze", 2°) and S is the surface of the solid bounded by the cylinder…

A: We need to calculate ∬SF→.dS which is the flux. Now, we can use the divergence theorem to find…

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: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A: Parametrize the three curves separately and c is the sum of the three integrals.

Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: The solid in the first octant bounded by the coordinate planes and the plane z = 8 – x – y dz dy dx

A:

Q: Evaluate JS yz + 4ryds where S is the surface of the solid bounded by 4x+2y+z=84, z=0, y=0 and x=0.…

A: Use the divergence theorem to find the surface integral,…

Q: y dV, where E is the solid bounded by the parabolic cylinder z = x² 14 - 2y. Find and the planes y…

A: Introduction: The goal is to assess the triple integral that is presented. And ∫∫∫EydV is the…

Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: If f′(0)=f′(2), find the difference c-2d for the following cubic spline S(x) with clamped boundary…

A:

Q: The solid bounded by x = y? – 1, z = 1 – y², z = 4 – x, and z = 0.

A: Given that,

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

A:

Q: Find y dV, where E is the solid bounded by the parabolic cylinder z = x° and the planes y = 0 and z…

A:

Q: 6. Evaluate the triple integral 2x2z +2yz dV where S is the solid that lies below paraboloid z = -r?…

A:

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: a) Let G be the wedge in the first octant that is cut from the cylindrical solid y² + z² ≤ 4 by the…

A: To Evaluate: ∫∫∫GxyzdV. Where G: y2+z2≤4, y=2x , x=0. As per policy, we are solving only thr first…

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: Calculate ff F.n dS where F x'yzi + 2xj + y?k in the solid region S bounded by the parabolic tube z…

A:

Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

A:

Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: T// Vx² + y² dV, where E is the solid in R3 bounded by the surfaces E z = x² + y² and z = 8 – x² –…

A:

Q: Find ||/ y dV, where E is the solid bounded by the parabolic cylinder z = x and the planes y = 0 and…

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. The solid bounded by z = 0, z = 1 – x², z = y and 2y + z = 12.

A: Given that  Region z=0,z=1-x^2 and 2y+z=12  To form a triple integral

Q: 6. Below is the solid bounded by the surfaces S1: z° = 16 – 2y S2: x = 4-y + z, S3: x = 1, in the…

A: Answer is mentioned below

Q: Find /// y dV, where E is the solid bounded by the parabolic cylinder z = 2 and the planes y = 0 and…

A:

Q: Use Green's Theorem to evaluate |(e* +y²) dr + (+r²) dy where C is the boundary of the region…

A:

Q: Find // y dV, where E is the solid bounded by the parabolic cylinder z = x? and E the planes y O and…

A:

Q: Sketch the region enclosed by the given curves. y = 5 cos(3x), y = 5 sin(6x), х%3D 0, x = T/6 y y 5t…

A:

Q: /| y dV, where E is the solid bounded by the parabolic cylinder z = 1° and the planes y = 0 Find and…

A:

Q: Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices A, B, C, D, E and O,…

A:

Q: 6. Below is the solid bounded by the surfaces S1:2° = 16 – 2y S2:x = 4-y + z, S3:x = 1, in the first…

A: Given a solid in space, we have to find the projection on the 1st quadrant.

Q: please help me as soon as possbile

A:

Q: Find II| y dV, where E is the solid bounded by the parabolic cylinder z = x² and the planes y = 0 E…

A:

Q: The volume of the solid generated by the curve y = e², between z = 2 and z =7 about the I - azis is…

A: Given curve is y=e-x  x=2 and x=7 about the x axis find the volume

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal…

A: The equation is u t…

Q: JS S is the surface of the solid bounded by the cylinder x = y² and the planes x + z = 1 and z = 0.…

A: Here we will use divergence theorem to find flux of given vector field across S In  a simple solid…

Q: c, y, z) = x²zi + xz'j+ y ln(x + 1) k, s the surface of the solid bounded by the 2z = 4, y = 3, x =…

A:

Q: Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = the planes x = 0, x =…

A: Here I am using simple tripple integration to solve this question.

Q: Find // y dV, where E is the solid bounded by the parabolic cylinder z = x? and E the planes y 0 and…

A:

Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

Q: S Find the voleime of the solid generated by revolving the region baunded by the given lines Cnd…

A: Hint: Try Disk Method to find the volume.

Q: The solid bounded by the surfaces S : -2(: – 2) = y² S2 : 1 = 5– 2y S3: r=0 S4 : y = 0 Ss : z = 0…

A:

Q: 6. Consider the solid Q bounded by the surfaces S1 : 1 = 4 – 22 S2 : 1+y = 5 S3 : 1 = 0 S4 : y = 0…

A: Solid bounded by surfaces: Double integration can be used to find the volume of a solid limited by…

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

A:

Q: //| y dV, where E is the solid bounded by the parabolic cylinder z = x² and the planes y = 0 E Find…

A: we have to find volume

Q: A 3 cm length silver bar with a constant cross section area 1 cm" (density 10 g/cm, thermal…

A:

Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…

Q: * Evaluate the sur face in tegral S F · d3, where + y?7 + :? and S is the boundary of the solid…

A: Given data: F→=x2i→+y2j→+z2k→ S is the boundary of the solid half-cylinder  0≤z≤1-y2, 0≤x≤2 Using…

Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

A: