Calculate the line integral fe F. dr, where F = (ry, r? + y? + 22, yz), and C is the boundary of the parallelogram with vertices (0, 0, 1), (0, 1,0), (2,0, -1), and (2, 1,-2). Note that this parallelogram lics in the plane z = 1-r- y. %3D

Q: (B) Integrate g(x,y,z)=x+y(x+2z) over the surface area of the region cut from plane x+2y+2z=5 by the…

A: What is Surface Integral: Surface integral is an iterated integration that is performed over a…

Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: = [ry, yz, cz] and C is 6- Evaluate the line integral fc F dr, where F e boundary of the hemisphere…

A:

Q: Find the area of the surface of revolution r(u, v)= 6sin(u)cos(v)i+ 6uj+6sin(u)sin(v)k, where 0SusT…

A:

Q: Evaluate the integral for y dx +z²dy + x²dz, where C is the triangular closed path joining the…

A: Stokes theorem:  Let C be a closed curve S be a surface enclosed by curve C. F is defined every…

Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, –2, 0),…

A:

Q: Integrate g(x,y,z) = 3x + 2y +z over the portion of the plane 4x+ 8y +z = 16 that lies in the first…

A: We have to find the value of the given integral.

Q: Use Stockes' theorem to calculate the line integral fc F · dr where F (1,4) = (3zy + eN i + (25° –…

A:

Q: use cylindrical coordinares to caiculate the +riple integral JJSW F(x,y,z) dv for the function f Cx,…

A: Consider the given function, fx,y,z=1784zx2+y2 And, x2+y2≤z≤28-x2+y2 We have to calculate the…

Q: Calculate the line integral fe F. dr, where F = (ry, x² + y² + z², yz), and C is the boundary of the…

A: Given F→=xy,x2+y2+z2,yz and C is the boundary of the parallelogram with vertices…

Q: Use Stoke's theorem to evaluate the integral xydx +2x 'dy-&r 'zdz where C is the boundary of the…

A:

Q: integrate ƒ over the given region. ƒ(u, y) = y - sqrt(u) over the triangular region cut from the…

A:

Q: Given the area bounded by the curve y^2 = 4x and y^2 = 8x − 8. Determine the centroid area bounded…

A:

Q: Evaluate the surface integral xyzdS where S is the part of the plane z = 1 + 2x + 3y that lies above…

A:

Q: Use Stokes' theorem to evaluate line integral| (z dx + x dy + y dz), where C is a triangle with…

A:

Q: Compute the surface area of the surface segment parametrised by x(u, v) = u² cos v, y(u, v) = u² sin…

A: Given, xu,v=u2cosv,yu,v=u2sinv,zu,v=u2where 1≤u≤3 and 0≤v≤2π To find the surface area.

Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, –2, 0),…

A:

Q: Evaluate the surface integral. /| x*yz ds, s is the part of the plane z=1+ 2x + 3y that lies above…

A:

Q: Evaluate the surface integral. I= 4xds Where S is the triangular region with verticies: (1,0,0), (0,…

A:

Q: Use Stokes' Theorem to find the line integral [((x² + 2y² ((x + 2y²)i + (y + 2²)j + (2 + 2x²)k) · dř…

A: Given that C is boundary of triangle with vertices 1,0,0,0,1,0,0,0,1 So, equation of the plane with…

Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

A: Given ∭x8ey dV

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A:

Q: Use Stokes' Theorem to find the line integral [((x² + x + 2y²)i + (y + z³)j + (z + 2x²)k) · dr where…

A: To Evaluate: The integral ∫C(x+2y2)i+(y+z2)j+(z+2x2)k·dr. where C is the boundary of the triangle T…

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…

A:

Q: Evaluate the integral for y*dx + z²dy + x²dz, where C is the triangular closed path joining the…

A: To evaluate the integral ∫Cy2dx+z2dy+x2dz where C is the triangular closed path joining the points…

Q: Verify that Green's Theorem is true for the line integral (x + y' ) dx – 5xydy for which C is the…

A: To verify Green's theorem for the line integral ∫Cx2+y2dx-5xy dy, where C is the boundary of the…

Q: Use Štoke's Theorem to evaluate the line integral - 2ydx +-6zdy + dz where C is the intersect | of…

A: Strokes theorem is ∫CF→.dr→=∫∫S∇×F→.N→dS=∫∫ScurlF→.N→dS x=rcosφy=rsinφ

Q: Find the area of the section of the surface x = u2, y = uv, z = v2/2 bounded by the curves u = 0, u…

A:

Q: 18. z = 4 – x2 – y², 0<z< 3; f (x, y, z) = x² / (4 – 2) - -

A: Use polar coordinates to solve the integral

Q: Solve for the area of the portion of the cylinder x = V1 – y², which lies between the planes z = 0…

A: Line integral

Q: Sketch the region of integrationRbounded by the paraboloidy=x2, the planey+z= 1and the xy-plane.…

A: We are given the following surfaces:paraboloid: y = x2plane 1: y + z = 1plane 2: z = 0 (XY-plane)We…

Q: Use Gauss's Theorem to find the surface integral OF •dS across the positively-oriented S sphere of…

A:

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

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: Express the surface integral as an iterated double integral by using a projection of S on the…

A:

Q: 1. Verify Green's theorem in the plane for $ (3x2- 8y,dx + (4y - 6xy)dy, where C is the boundary of…

A:

Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

A:

Q: Let S be a square plate with boundary C having length of each side as 2 units, lying in the plane z…

A:

Q: Evaluate line integral f,dr where f=(x2+y2)i and c is the rectangle in the xy plane bounded by…

A:

Q: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: use a double integral ond that is above by the plane f(x,y) = 4 – x - y and below by the rectangle R…

A: Volume of the function z=fx, y and region R is  V=∫∫Rfx,ydA

Q: Find the area of the part of the plane z=3x+5 y+3 that lies above the region R=(x,y) 2≤x≤3; 1sys5.

A: The given plane is z=3x+5y+3. Differentiate partially with respect to x, y respectively to obtain…

Q: Use Stockes' theorem to calculate the line integral fe F.dr where F (2.52) = (szy + e)i + (2 – Iny)3…

A:

Q: Use Stokes' theorem to evaluate line integral (z dx + x dy + y dz), where C is a triangle with…

A: Consider the provided question, We have to evaluate the given integral by using the stokes theorem,…

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4x + 4y R:…

A:

Q: Evaluate |[A.ndS where A = 2xyi+yzj+xzk and S is the surface of the region bounded by x = 0, y = 0,…

A:

Q: Find the area of the surface f(x,y)= x² + 3y over the triangular domain bounded by the x-axis, the…

A:

Q: Find the line integral of z2 dx + y dy + 4y dz, where C consists of two parts, C, and C,. C, is the…

A: Given line integral ∫Cz2dx+ydy+4ydz, where C consists of two parts C1 and C2. C1 is the intersection…

Q: Evaluate the surface integral. x dS, S is the triangular region with vertices (1, 0, 0), (0, –2, 0),…

A:

Q: Find the surface area of z =1-(x^2)-(y^2) that is above the xy plane

A: Given equation of plane is  z=f(x,y)=1-x2-y2 we have to find the surface area above xy plane.