ulate F · dS if F(x, y, z) = x²ye²i + xy²j – 2xye²k, where bounded by the coordinate planes and the planes r = 4, y = 3, an

Q: Calculate F . dS where F = (e sin y, eº cos y, yz²) and S is the surface of the box bounded by the…

A: Here, F=<exsiny,excosy,yz2>

Q: (b) Integrate the function g(x, y, z) = x + y + z over the surface that is described as follows:…

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Q: Use stokes theorem to evaluate f.dr where f = (4z+y, 3x, 7y) and C is the curve of intersection of…

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Q: [| fcx. y. 2) ds 1. f(x, y, z) = z²; o is the portion of the cone z = /x² + y² between the planes z…

A: Solution is in step 2

Q: Evaluate fc F dr where F (x, y, z) = xy i + yz j zx k and is the twisted cubic given by

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Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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

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Q: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

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Q: Find Ix, Iy Io X, and y for the lamina bounded by the graphs of the equations y = Vx, y = 0, x = 4,…

A: INTRODUCTION: The formula of the radius of gyration of the lamina of the density function ρ is given…

Q: The equation of the tangent plane to the surface f (x, y, z) = xe cosz - z -1= 0 at the point…

A:

Q: Use cylindrical coordinates. Evaluate IIL Vx²+ y2 dv, where E is the region that lies inside the…

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

Q: 8. (x – y) dV, where E is enclosed by the surfaces z = x² – 1, z = 1 – x² , y = 0, and y = 2 E

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Q: a) A laminar with density &(x, y) = lies in the first quadrant is bounded y3 by two circles a2 + y²…

A: Given that, the density function is: δ(x,y)=xy3 Now, Ix=∫∫x δ(x,y) dy dx   =∫∫xxy3dy dx   =∫∫x2y3dy…

Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 0, y = 2, x =…

A: The value of I0,Ix,Iy.

Q: Verify Stokes's Theorem for F = z²î+ x²j + y²k and S is the surface z2 = x2 + y², y 2 0, and 0 <…

A:

Q: Integrate the function F(x,y,z) = 2z over the portion of the plane x + y +z=5 that lies above the…

A: given, f(x,y,z)=2z.

Q: The equation of the tangent plane to the surface f (x,y,z)= xe" cosz- z-1= 0 at the point…

A: Given surface is xeycosz-z-1=0 and the point is A1,0,0 find the equation of tangent

Q: Integrate F(x, y, z) = z - x, over the cone z = sqrt(x2 + y2), 0&lt;= z &lt;=1

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Q: a) A laminar with density d(x, y) lies in the first quadrant is bounded y3 by two circles r² + y² –…

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Q: The solid bounded by the surfaces: corresponds to: A) B) I 42 S₁: -2(2-2) = y² S₂: x = 1+ 2y S3: x=0…

A: Any point on the three dimension is represented as x, y, z. A surface in the three dimension is…

Q: Integrate the given function over the given surface. G(x,y,z) = x over the sphere x2 +y2 +z? : = 16…

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Q: the value of the double integral ∬ R (y^2 + x^2) dA, where R is a circular disk defined by x^2 + y^2…

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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: Verify Stokes's Theorem for F = z²î + x²j + y?k and S is the surface z² = x2 + y2, y 2 0, and 0 szs…

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Q: Integrate R(x,y,z)=x (xy2 +z) over the surface of the cylinder x2 + y2 = 9 that lies between the…

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Q: F(x, y, z) = tan-'(x?yz²)i + x²yj + x²z?k, S is the cone x = V y2 0 <x < 4, oriented in the…

A: Define curve C with boundary curve: r→=4i^+4costj^+4sintt^

Q: theorem find the value of f F.dr ere F(x,y) = (e* – y³)i + (cosy + x³)j and C is the nded by the…

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Q: Use cylindrical coordinates. Evaluate Vx2 + y2 dv, where E is the region that lies inside the…

A:

Q: 17 The solid bounded by the surface y =x² and the planes y+z=4 and z = 0.

A: To find the volume of the solid

Q: The solid in the first octant bounded by the coordinate planes, y+ z = 4, and x = y.

A: The objective is to find the volume for y+z=4,x=y The volume of the integral formula is,…

Q: (ii) Use Stokes' Theorem to evaluate SF · dr, where F(x, y, z) = x²zi+xy²j+z²k and C is the curve of…

A: Given function is F(x,y,z)=x2z i^+xy2 j^ +z2k^ . Plane: x+y+z=1 Cylinder: x2+y2=9 The objective is…

Q: Use cylindrical coordinates. Evaluate | Vx²+ y2 dV, where E is the region that lies inside the…

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Q: 11. Integrate G(x, y, z)=x√y² + 4 over the surface cut from the parabolic cylinder y² + 4z = 16 by…

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Q: Use Stokes's Theorem to evaluate f. F dř where F(x, y, z) = (x- y) i+ (y-z)j+ (z - x) k and S is the…

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Q: triple integral /// y dV; G is the solid enclosed by the Evaluate the plane z = y, the xy-plane, and…

A: Given integral is ∬∫Gy dV ; G is the solid enclosed by the plane z=y, the xy-plane and the parabolic…

Q: F(x, y,z) = (2xz) i+(1-4xy“) j+(2z-z) k and S is the surface of the solid bounded E z6%- 2x2 – 2y²…

A: Given function is: F=2xzi+1−4xy2j+2z−z2k Here S is the surface of solid bounded by the below…

Q: Integrate the function F(x,y,z) = 6z over the portion of the plane x + y + z = 6 that lies above the…

A:

Q: XII. $F•d$ where F = (x,y,z²) and S is sphere of radius 2 with center at 0.

A: F→=x,y,z2, surface S is sphere of radius 2 with centre O=0,0,0To find: ∯SF→.dS→

Q: Integrate the function F(x,y,z) = 4z over the portion of the plane x +y+z=6that lies above the…

A: F(x,y,z) = 4z Limits of integration x varries from 0 to 3 y carries from 0 to 3

Q: eVx² +y?+z? T(e4 – e)(x² +y² + z?) Let f(x, y,z) Let S be the solid bounded by the xz plane and the…

A: Here we can use spherical coordinates to find the value of the integral. In spherical coordinates…

Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

A:

Q: The solid in the first octant bounded by the coordinate planes and the plane z = 3 – x –y dz dy dx

A: Answer is:∫03∫03-x∫03-x-ydzdydx Proof is attached below.

Q: 24. F(x, y, z) = -xi-yj+z° k, Sis the part Vx² + y² between the planes z=1 and z= 3 with downward of…

A: Given that,  F(x,y,z)=-xi-yj+z3kAnd the cone is, z=x2+y2⇒z2=x2+y2Let, f(x,y,z)=x2+y2-z2

Q: Integrate the function F(x,y,z) = 6z over the portion of the plane x+y+z=6 that lies above the…

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Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

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Q: Integrate G(x, y, z) = x, over the parabolic cylinder y = x2, 0 &lt;=x&lt;= 2, 0&lt;=z&lt;=3.

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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: ane for the level surface f(x,y,z) = 4x2 + cos (3y) + In (5z) = c %3D O.500z - 44 518

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Q: integrate the given function over the given surface. H(x, y, z) = x2√(5 - 4z), over the…

A: Application of integration: We can use cylindrical coordinate to find a parametric equation for the…

Q: Find SS F dS where F(x, y, z) = z i+(3x – 1)j+ yk and S is the portion of the plane x + y + z = 1…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.