(b) A = 2rza, + 3z sin ø a, – 4 rcos o a̟ and S is the surface of the wedge 0

Q: 2. Find the surface area obtained by rotating the curve (a) y = sin(Tr) around the x-axis for 0 <x <…

A: The objective here is to find the volume of area obtained by the rotating the given curves in each…

Q: The area of the surface obtained by revolving the curve y = x3 for 1<x<8 about the y-axis, is given…

A: Surface area obtaining by x=f(y) from x=a to x=b is about y-axis given in step 2.

Q: 13 - x² – y? at (3, 2, 0), then If the point (1, 1, k) lies on the tangent plane to the paraboloid z…

A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

Q: O (y +ev* )dx + (2x + cos y)dy , where C is the boundary of the region enclosed by the parabolas y =…

A:

Q: QUESTION 8 Find the area of the cylindrical surface in Xyz-space where a point (X,y,z) on the…

A: Find the surface area of the cylinder in xyz-space where a point x, y, z on the surface satisfies…

Q: The area of the surface generated by revolving the curve y=x² if 0<x<2 about the y-axis is given by…

A:

Q: Find the area of the surface generated by e + e -y revolving the curve x = 2 0sys In 6 about the…

A: To find the surface area generated by revolving the curve x=ey+e-y2,0≤y≤ln6 about the x-axis. We…

Q: 12. Consider the arc L : y = 1 + cos z from (0, 2) to (,1). Which of the following integrals give…

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Q: 5) Consider the surface S shown in the graph, whose parametrization is given by by: r(u, v) = (v²,…

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Q: 1. Evaluate the integral x(у — 1) dz where C is a curve from z = 2 to z = -2 following a semicircle…

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Q: (9) Evaluate // 2² + y² + z²)³/? dV where D is the solid region in the first octant between the two…

A: Volume between the two spheres using spherical coordinates

Q: U SIII u' cos u?, EXAMPLE 6.6.3 For a surface of revolution defined by x u! oin o? COS 3 flol) aub…

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Q: The circle of radius 3 centered at the origin Ex. to calculate the area of the given region.

A: Given: The region between x-axis and the cycloid parametrized byr(t)=t-sin t, 1-cos t  for 0≤t≤2π

Q: 5. Suppose r = r(0) cos(0) and y = r(0) sin(0), where r(0) is sufficiently smooth, and suppose x = a…

A: We are given that y=rθsinθ and x=rθcosθ, where r(θ) is sufficiently smooth and α≤θ≤β . We have to…

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: The surface area of the surface generated by revolving y=1-x? for 0<x<1 about the x- axis is None s=…

A: surface area S =∫012πy.ds where ds=1+(dy/dx)2

Q: (a) Given a surface function, z(x, y) == + xy with x cos0 and y= sin 0, 2 %3D az and əz (i) find ax…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 5) Evaluate the integral (e* - y) dx + (sin y + x)dy using Green's theorem where Cis bounded by y =…

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Q: The region between the curve y = Vxe- and the x-axis for0 <r<∞ is rotated about the r-axis to create…

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

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Q: Question 4 The surface integral 3x + 6y do V1 + ely + 422 over E= {(r, y, z) E R³ | 0<I<1, r -1 <yS…

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Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

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Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

Q: 1. Find the area of surface that is generated by revolving the portion of the curve y = V4- r2…

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Q: - y² + 4y + 49 and The base of a solid is the region in the zy-plane bounded by the curves a : x =…

A: Given , base of a solid = region in the xy-plane bounded by  the curves…

Q: 6. C is the curve of intersection of the plane 4x + 5y+ z = 0 with the cylinder x2 + y? = 4 directed…

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Q: .... ........ 4.8. Find the area of the surface generated by revolving the curve x = cost, y =…

A: See the details solution in below

Q: 1. Consider the spiral ramp r(u, v) = ( u cos v, u sin v, v ) with 0 < u < 3 and 0<v < 2n. Use a…

A: Consider the given information.

Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

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Q: 8) Consider the solid Q that is generated in the first octant by the surfaces S₁: (x - 2)² + (y-2)²…

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Q: Problem. 9: Use the Divergence Theorem to calculate the surface integral || F. dS, where S F(x, y,…

A: Given the field equation, Fx,y,z=xz2i+y33+coszj+ x2z+y2k The surface S is the top half of the sphere…

Q: Consider the line integral L(- In(2² + y°\j+ tan '(2)i). dr where C is the positively oriented…

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Q: 5. On the surface z-3x^2+2y^2 (an elliptic paraboloid), (x,y) changes from (1,1) to (0.99,1.02). Use…

A: Since you have asked multiple questions, we will solve the first question (Question 5) for you. If…

Q: 1.2. The area of the region bounded by the curves sin r, y = cos r, I= 0 and a equal to A. 1.4142…

A: Given curves are y=sinx, y=cosx ,x=0 and x=π/4

Q: 3. By using Green's Theorem in the plane, evaluate | (y - sinx) dx + cos x dy where C is the…

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Q: Find the area of the surface generated by e +e -y eY + e -y in the X= revolving the curve x= -In 3…

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Q: The surface area of the surface generated by revolving y= 1-x2 for 0<x<1 about the x - axis is S = […

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Q: 3. Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y…

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Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

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Q: Flux Integrals (sin y cos zi+e² cos zj+cos y ln(1+x²)k) ·N dS, where S is the sphere x2 +y? + z² = 1…

A: Consider the equation

Q: u' cos u?, r? EXAMPLE 6.6.3 For a surface of revolution defined by x u sin u?, x3 = f (u'), where f…

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Q: 3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions…

A: The Laplace equation is given by: r2∂2u∂r2+r∂u∂r+∂2u∂θ2=0 The boundary conditions are: ∂u∂θr,0=0,…

Q: Let R be the region inside the ellipse x = 4 cos 0, y = 3 sin and outside the circle x = 2 cos 0, y…

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Q: u' cos u?, x? EXAMPLE 6.6.3 For a surface of revolution defined by x u' sin u?, x³ = f (u'), where f…

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Q: The surface area of the surface generated by revolving y 1-x? for 0Sr<1 about the x-axis is S=…

A: Rule- If the curve y=f(x), a≤x≤b is rotated about the x−axis, then the surface area is given by

Q: Let R be the region inside the circle x = 5 cos 0, y = 5 sin 0 and outside the %3D ellipse x = 2 cos…

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Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

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Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

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Q: A solid lies above the cone 2z = v x² + y² and outside the sphere x2 + y² + z² = 6z. Write a…

A: Given: Solid lies above the cone is 2z=x2+y2 and outside the sphere x2+y2+z2=6z

Q: 1. The area under the curve with parametric equations z = 1 + t?, y = l(2 – t) in the interval 0sts1…

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