Verify stokes theorem for F = (2x- y)i – yz'j - y zk over %3D the upper half surface of the sphere x+ y + z´ =1 bounded by the Projection on the xy-plane. %3D

Q: Let F = (x,y) and C be the circle of radius 5 centered at the origin oriented counterclockwise.…

A: Let F=x,y and C be the circle of radius 5 centered at origin oriented counterclockwise. We have to…

Q: Use Stokes' Theorem to evaluate for F. dr. F(x, y, z) = 5xyi + 5yzj + 5zxk C where is the triangle…

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Q: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

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Q: How do you calculate the area of a parametrized surface in space? Of an implicitly defined surface…

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

A: Given that the equation is  y=1sin(πx)+5 bounded by x=0,x=2 and y=0.

Q: 1: Describe the solid bounded by the sphere ² +y² + z² = 9 and the pla 2 over the xy-plane using %3D…

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Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

A: For the detailed solution of the problem follow the next steps.

Q: AREA UNDER THE PLANE 6x +4y +z = 12 above the disk W/ BOUNDARY CIRCLE

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Q: Find the polar moment of inertia about the origin of a thin triangular plate of constant density d =…

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Q: Verify Stokes theorem for F = (xy -x2)î + yx?j in the region in the xy-plane bounded by y = 0,x = 1…

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Q: A thin plate of constant density covers the region bounded by the ellipse x2/a2 + y2/b2 = 1, a…

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

A: We need to find co-ordinates of centroid.

Q: integral Over the é dz Z-2 the Compute %3D Curve C below lm (2) Relz)

A: In the given question we have to find the value of the integral I over the curve C. and the given…

Q: Find the volume of the solid bounded from above by the surface z = (64 − 4x^2 − 9y^2)^(1/3) and from…

A: To find - Find the volume of the solid bounded from above by the surface z = 64 - 4x2 - 9y213 and…

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

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Q: Calculate the line integral x y dx + x² y³ dy where C is the triangle with vertices (0,0), (1,0),…

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Q: 5. Use our Early Parameterization step by step including sketch of the surface to evaluate the…

A: Given that The equation of cylinder in the xz-plane as x2+z2=1 Also, the given surface integral lies…

Q: Find the võlume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We can solve this using disk method for finding volume of the given question

Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

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Q: Use Green's Theorem to calculate the work done by the force F (x, y) = 3i + (x' + 1)j on a particle…

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Q: 4. Consider the surface given by z = x x²esin y. (a) Find the equation of the tangent plane to z =…

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Q: Let R be the solid region inside the cylinder x^2 + y^2 = 1 and inside the paraboloid z = 5-x^2-y^2…

A: Given,x2+y2=1Using cylindrical coordinates,x2+y2=r2 0≤r≤10≤θ≤2πNow, z=0z=5-x2-y2z=5-r2 0≤z≤5-r2dv=r…

Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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Q: calculate the surface area of the solid obtained by rotating the curve over the g.iven interval…

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

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Q: C is the intersection of the cylinder with equation (x-1) + z? = 4 with the plane x + 3y +z = 9 in a…

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Q: Use Stokes' Theorem to evaluate the line integral (y + 2z)dr + (x + 2z)dy + (x+ 2y)dz where C is the…

A: Given intgeral. ∫Cy+2zdx+x+2zdy+x+2ydz The Curve is formed by the intersection of the sphere…

Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

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Q: Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the…

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Q: 3) Find the area of the surface that results from rotating the curve Y = sin MX, 0 s X < 1 about the…

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Q: a) Evaluate ||| x²yz dV, where G is solid in the first octant that is bounded by parabolic cylinder…

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Q: Find the polar moment of inertia of the region in the xy plane bounded by x² - y? 1,x2- y2=9, xy…

A: Solution is in step 2

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…

A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…

Q: S is the surface with parametric equations x = Зи+ v, у — Зи— v, z = uv for (u, v) in the region D…

A: The integral of a scalar valued function can be calculated as follows, using the parametrization:…

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: 1) Let h(x, y) = x* – 4xy² – 2x² + 8y². Find and classify all local extrema of the surface using the…

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Q: - S is the surface with parametric equations x = 3u+v, y = 3u-v, z = uv for (u, v) in the region D…

A: We will find out the required value.

Q: Find the Surface Area rotating around the y-axis

A: Given curve is

Q: 3. Find the area of the surface generated by revolving the curve about the given axis: x = g(y) =…

A: ds= sqrt(1+(dx/dy)^2)

Q: (a) Integrate g(x,y,z) = lnx'+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Cvaluate AP G is a solid in the first octant bounded by the plane y+ z = 2 and the urface y = 1 -…

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Q: 3. Evaluate the triple integral || ryz dV; G is the solid in the first octant that is bounded by the…

A: To evaluate the given integral ∫∫∫Gxyz dV. The limits are given as  z=0 to z=2-x2 and y=0 to y=x and…

Q: Express the double integral | (1+x)dA, R. where R is the region in the upper half-plane (i.e. y 2 0)…

A: Need to express ∫∫R(1+x)dA between circles x2+y2=9 and x2+y2=16 in polar…

Q: The area of the surface obtained by rotating the curve y = et +e asxsb, about the x-axis is 1/2 e2 +…

A: Find the surface area rotating the curve about x axis

Q: Let C be the curve of intersection of the cylinder x2 + (y- 1)2 = 1 with the plane y = z, traversed…

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Q: Find the exact area of the surface obtained x=t°, y =t 0<t<lby rotating about the x- аxis.

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