3. Evaluate xyz dS, where S is the part of the plane z = 6- y that lies in the cylinder x +y? = 4.

Q: Set up |// x² dV using cylindrical coordinates where E is the E solid that lies within the cylinder…

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Q: 2. Give iterated integrals for (xz*)dS where S is the part of the cylinder x² + y = 9 above the…

A: Given that x2+y2=9 and the part of the cylinder which is above XY plane implying that z > 0. We…

Q: (4) Let S be the surface parametrized by I= r cose y =r sin e 2= 30 where and Evaluate the integral…

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Q: Evaluate the surface integral.     Sz2 dS, S is the part of the paraboloid  x = y2 + z2  given by…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y2+ 5z2 and the…

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Q: 4. Set up the integral that gives the surface are of the figure obtained by rotating around the…

A: We need to set up surface area integral.

Q: The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of…

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Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

A: Given slant height l. Let r and R be the radii of the frustum. Let h be the height of the frustum.…

Q: The sphere of radius a centered at the origin is expressed in Cartesan coordinate as x +y² +z? = a².…

A:

Q: The area of the surface obtained by revolving the curve x= Vy+3 for a-3.) 2x /4y + 12 dy 2л уу +3 dy…

A: Consider the curve x=y+3 for a≤y≤b. Find the area of surface when curve is rotated about y-axis.…

Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

Q: 9. Find the characteristics of the equation hx = bd and determine the integral surface which passes…

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Q: 1 1) To find the exact area of the surface obtained by rotating the curve y = 2, 0<x < 12 about the…

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Q: 16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: To compute the surface area of the surface obtained by revolving the given curve about the axis x =…

Q: Set up the following triple integral, but do not calculate it: a solid above the xy-plane, inside…

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Q: An integral expression for the area of the surface generated by rotating the curve y=√x, 0≤x≤ 1…

A: Given: y=x3, 0≤x≤1 To find the area of the surface generated by rotating curve y=x3 and 0≤x≤1 about…

Q: 7. Find the length of the curve y (r + 4)/2 on the interval [0,3] 8. Set up, but do not evaluate, an…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the surface integral. y ds S is the part of the paraboloid y = x² + z² that lies inside the…

A: The projection of S onto the xz-plane is the disk D=x,z: x2+z2≤9. We have to calculate the surface…

Q: (b) Set up a definite integral that is equal t length of the portion of the parabola y which serves…

A: Introduction: The washer method is used to calculate the volume enclosed by two functions. In this…

Q: Consider the surface of revolution formed by revolving the curve y = 1/x, 1 < x < a about the…

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Q: 2. a. Calculate the surface integral of /(x.y,z) = obtained by parametric equation: over the full…

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Q: F(x, y, 2) = xi + yj + 9k, s

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral (5 + Væ…

A: The function is: ∫065+x+123 dxn=10

Q: Please help me solve this problem!  Thank you!!!

A: From the given data, the surface area of the surface S is parametrized by

Q: 8. If the density of ants on the surface of the paraboloid z = x? + y² (0<z<4m is given by f(x,y, z)…

A: x2+y2=zf(x,y,z)=32(x2+y2)(ans/m2)

Q: 3. Suppose the curve x = t³ – 9t, y = t+3 for 1 <t < 2 is rotated about the x-axis. Set up (but do…

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Q: Evaluate the surface integral SP ( – 2) // where S is the portion of the cylinder r2+22 = 1 above…

A: It is given that S is the portion of the cylinder x2+z2=1 above the xy plane between y=1 and y=2.

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: Here we will cylindrical co ordinate system to parametrize the surface  x=r cosθ , y = r sinθ , z=z

Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

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Q: Consider the following curve. y = x, 0sxs 3 Set up an integral in terms of x that can be used to…

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Q: need to find the limits of integration in terms of ρ, φ, and θ.

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Q: 2 Sphere S to be the top half of sphere · x² + y² + 2² SS₁zdS /5 calculate the integral.

A: The given Surface is the top half of the surface x2+y2+z2=a2. To Evaluate: ∬zdS.

Q: Solve the following surface integral (use definition): F = [32 6 6rz] with parabolic cylinder…

A: Given, F = 3z2i +6j + 6xz k And surface S is ,S:y= x2  with 0 &lt; x &lt; 6 and 0 &lt; z &lt; 1…

Q: Use a line integral to find the area of the surface that extends upward from the parabola y = x² (0…

A: We have to use a line integral to find the area of the surface that extends upward from the parabola…

Q: . Express the area of the portion of the paraboloid z=x² + y? that is above the xy plane and below…

A: Asked questions is solved.

Q: The area of the surface obtained by revolving the curve x Vy+3 for as-3.) n(y +3) dy 1+ 4y + 12 dy…

A: Explained below

Q: Express the double integral || (x +1)dA, where 2 is the region in the upper half- plane (i.e. y20)…

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Q: T Express the surface area of the surface obtained by rotating the graph of y = 4 sin (x) for 0 ≤ x…

A: Recall: Surface area SA=∫ab2πy1+dydx2dx We have, y=4sin(x), a=0, b=π6

Q: x = 0, y = 1, X = %3D about the line y = 1 can be computed using the method of disks or washers via…

A: According to the problem, we have

Q: Set up, but do not evaluate, an integral that's equal to the surface area of the surface formed by…

A:

Q: Find the area of the surface generated by revolving the curve x = 4 1 from 8y 3 < y< 5 about the…

A: When a function is of the form x=g(y) and you are revolving around the x-axis, the interval is c≤y≤d…

Q: ху — 4, 1 <x< 8

A: Surface area.

Q: tes to evaluate the triple integral e Vz² + y² + pounded by the spheres z² + y² + z² = 4 and z? + y…

A: Given, ∫∫∫Ee-x2+y2+z2x2+y2+z2dV E is the region bounded by spheres x2+y2+z2=4 and x2+y2+z2=25.

Q: 1. Evaluate the following surface integrals: (a) (x + y) dS, 0 : part of the surface 2x + 3y + z = 6…

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Q: Compute the surface area of the cone generated by revolving c(t) = (2t + 2, 6t) about the x-axis for…

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Q: By using double integrals, find the surface area of plane + y² -+z=c that lies inside a a the…

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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: True or false. The value of the surface integral, S k dS, where k is a constant, is equal co the…

A: The given statement is The value of the surface integral ∬Sk dS, where k is a constant , is equal to…

Q: Express the area of the surface obtained by rotating the curve y=in cse(2x) between x= and x= about…

A: surface area about y axis S=∫ab2πxds ....(1) where  ds=1+(dydx)2dx