6) Use Stokes' Theorem to compute ,(V × F) · ndS where S is the portion of the tetrahedron bounded by x + y + 4z = 8 and the coordinate planes with z > 0, n upward, F=< y², y + 2x, z?

Q: (5) Evaluate F- dr using Stokes' Theorem, where F(1, y, 2) = -y?i + xj +2²k and C is the curve of…

A:

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

A:

Q: A large conducting cone ( 0=30° )is placed on a conducting plane with a tiny gap separating it from…

A: A large conducting cone is placed on a conducting plane with a tiny gap separating it from the plane…

Q: (a) The moment of inertia of a surface about Sls x? + y? dS. Find the moment of inertia cylinder x?…

A: (a) Given, the suface z=xy lying inside the cylinder                         x2+y2=3.

Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, O=t/3, 0<¢<a H= 2r cosO sino…

A: This question is about application of Stokes theorem

Q: 311. Evaluate surface integral r*z+y° z}dS, where S is hemisphere x? + y? +z? = a², z 2 0. Correct…

A:

Q: I y dV, where G is the solid enclosed by the plane z = y, the xy-plane, and the parabolic cylinder y…

A:

Q: I = y dx + (z — х) dy — ydz, Jc

A:

Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, e= T/3, 0<¢<a H= 2r cosO…

A: This question is about application of stkoes theorem

Q: Question 7 (1 Let C be the curve of intersection of the cylinder x2 + (y - 1)2 = 1 with the plane y…

A:

Q: he C +y* +z*)i dzdydz The product of the triple integration (using spherical coordinates)

A: Given

Q: Q2) Evaluate each side of Stokes theorem for a portion of cylinder : p=2m 0<¢<a /3, 1<z<2 Н-Iz /2пр…

A: according to stokes theroem closed linr integral of H is same as the surface integral of curl of H.…

Q: 19. Find the z coordinate of the center of mass of the wire represented by the parametric equations…

A:

Q: Evaluate the cylindrical coordinate integral. 1/2 18 1/r cos 0 dz r dr d0 0 9 1/?

A: Given that triple integration problem or cylendrical coordinate problem .we use simple integration…

Q: At a point in an incompressible fluid having spherical polar co-ordinates (r, 0, 4), the velocity…

A: In orthogonal curvilinear co-ordinates i.e. when  u, v, w are expressed in terms of rectangular…

Q: 2² + y° = 1 = 2' - y %3| = z + y? = 1 +E z = I +y ² + y² + z² = 1 = 2° + y? circular cone sphere…

A:

Q: Q2) Evaluate each side of Stokes theorem for a portion of cylinder : p=2m 0<¢ <a /3, 1<z<2 H= I z…

A: according to stokes therem, line integral(H.dl)= surface integral(curl(H).ds) for evaluating line…

Q: Consider the cylinder x² + y² = 1, and let S₁ be the part of the cylinder that lies between the…

A: The given surface is S=S1∪S2, where S1 is the part of the cylinder x2+y2=1 that lies between the…

Q: / Use Stokes theorem to evea luarte the SS Canl F.n ds, S being that Part of the Sar face of the…

A: Solution::

Q: As shown in the picture at right, a solid is bounded below by the xy-plane, above by the sphere x² +…

A:

Q: CurlF dS x+y' +z =9, z20 se Stokes' Theorem to compute s for the hemisphere intersected with the xy-…

A:

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

A:

Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

A:

Q: c) Use the cylindrical coordinates to evaluate the triple integral. √9-x² 3 So So x+2 x+²y dz dy dx

A:

Q: 1. A wire is parametrized by (t, 5t – 3,3 – t2) from 0 st<1. (a) The density of the wire is given by…

A:

Q: 10. Use Stokes' Theorem to evaluate ||(V×F)· dS where F= (z,2x, y) and Sis the hemisphere of x' + y?…

A:

Q: 2 Find an equation for the circular cylinder 4x + 4y = 9 in cylindrical coordinates. Select one: a.…

A: Given:4x2+4y2=9  →1For cylindrical co-ordinate,we  will considerx=r cos θy=r sin θ

Q: Express [[[y dV in cylindrical coordinates, where is the solid that lies between cylinders x +y = 1…

A: In this question we required to find volume of region bounded by above 2 given circle and the plane…

Q: 3. Use Stokes' Theorem to evaluate F.dr where C F = -yz i+ (4y+ 1) j+ ryk and C is is the circle of…

A: According to Stokes' Theorem: Let S be an oriented surface with unit normal vector field, N, and…

Q: Question 7 ( Let C be the curve of intersection of the cylinder x2 + (y - 1)2 = 1 with the plane y =…

A:

Q: Express fffydV in cylindrical coordinates, where N is the solid that lies between cylinders +y -1…

A: Here we use Jacobian to convert this integral into cylindrical coordinate.

Q: Ise spherical coordinates. /I/ Vx² + y2 + z² dv, where E lies above the cone z = Vx² + y2 and…

A: we have to find the volume of ∬∫Ex2+y2+z2 where E is the region that lies above z=x2+y2 and between…

Q: [₁ F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + xzj + (x +…

A:

Q: Q 1. Use spherical coordinates to evaluate the triple integral x dx dy dz here D –{ (r u z) E R3 .…

A: First we have to understand relation between Cartesian coordinates (x,y,z) and spherical…

Q: A closed curve C is the intersection of the cylinder x? +y? = 1 and the plane S : 2y+z = 2. 1)…

A: This question is about application Stokes theorem

Q: 1. Compute ff(V × F) - dS, where S is given by r² + y²+ (z – 1)² = 2 and z > 0, and F(r, Y, z) =…

A: Given: S is given by x2+y2+z-12=2  and z≥0 Fx,y,z=-esinzy,x+sinz,cosx

Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

A:

Q: Use cylindrical or spherical coordinates to evaluate the integral. 4-y² /8–x²-y² 19. z? dz dx dy 0.…

A:

Q: Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION…

A: Solution

Q: 10) Find the flux of V x F across S as easily as possible. S is the portion of z = 4 – x2 – y² with…

A:

Q: 3. Suppose F z = 4 – a? – y? above the r- y plane, oriented upward. Calculate fe F dĩ in two ways:…

A:

Q: Question 5 2 4-y² cV8-x2-y? Use cylindrical or spherical coordinates to evaluate the integral. J.J.…

A:

Q: 5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

A:

Q: Q1/ Find the volume of the solid generated by revolving the shaded region about the x- axis for the…

A: To find:- Volume of solid  generated by revolving the shaded region about x axis by disc method…

Q: Integrate f(x.y) = /16 - x over the smaller sector cut from the disk x2 + y2 s 16 by the rays 0= and…

A: In the question we have to evaluate the value of integral.

Q: 7. Use spherical coordinates to find ||| z dx dy dz where E is the solid defined by E Os Vr* +y³ <z…

A:

Q: State the Stokes' Theorem. Ise the Stokes' Theorem as stated in (a) to evaluate the lin |F- dř here:…

A: We have to write the stokes theorem and using it We have to find the given line integral according…

Q: Without using the formula (Stokes), calculate l=∂S∫F(x).T(x)dl, where F(x) =x1x2i + x2x3j + x1x3k, e…

A: Consider the given : F→=x1x2i^+x2x3j^+x3x1k^ over the surface of northern hemisphere x12+x22+x32=16…

Q: 10. Use cylindrical coordinates to evaluate SS S(x+y+z) dV where E is the solid enclosed by the…

A: The region

Q: (a) To change from cylindrical coordinates to Cartesian coordinates, we use the equations Ox = r cos…

A: We will find out the required solution.

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.