Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 5zi + xj + 2yk across the surface S: r(r,0) =r cos Oi +r sin 0j + (25 -) k, 0srs5, 0s0s2n in the direction away from the origin.The flux of the curl of the field F is(Type an exact answer, using n as needed.)

Stoke' s theorem ∫CF.dr =∫∫scurl F .ds Given F=5z , x , 2y and r =r cosθ , r sinθ , 25-r2 ;…

Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F = 5zi + xj +2yk across the surface S: r[r,0) =r cos 0i +r sin Đj + (25 -7) k, Osrs5, 0s0s2z in the direction away from the origin.

Use the surface integral in Stokes Theorem to calculate the flux of the curl of the field F = 5zi + xj +2yk across the surface S: r[r,0) =r cos 0i +r sin Đj + (25 -7) k, Osrs5, 0s0s2z in the direction away from the origin.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

See similar textbooks

Related questions

Q: Use the vector field F(x, y) = x 2e yi + cos x sin yj and Green’s Theorem to write the line integral…

A: Counterclockwise is the direction opposite to that in which the hands of a clock travel; movement in…

Q: Evaluate the surface integral ∬SF⋅dS for the given vector field F and the oriented surface S. In…

A: Compare the given equation with general equation and find the value of P, Q and R.

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = (y +z*)i+…

Q: Compute the line integral of the vector field F(r, y, z) = (x + 2y + 3z) i+ (2x + 5y)j+(z – 3y)k…

A: As per policy, we will solve the Question 4 only please repost it to get solution of Question 5. In…

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: F =…

Q: Let S be the part of the plane 3r + ly +z = 3 which lies in the first octant, oriented upward. Use…

A: given plane 3x+y+z=3 which lies in the first octant oriented upward. use stokes theorem to find the…

Q: 3/ MATH

Q: 1. Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around…

A: Circulation of vector field F along curve C =∫CF→dr→ According to stokes theorem…

Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

Q: Find the flux of the field F(x, y, z) = z2 i + x j - 3 z k outward through the surface cut from the…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across…

Q: Find the flux of the vector field F (x, y, z) = (e-y, -y, x sin z) across the positively oriented…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = +z)i+ (x…

Q: Use Stokes' Theorem to compute the flux of the curl of the vector field F = (e² – y, x + e²",…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = zi +…

Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

Q: Let S be a simple closed surface in R' that encloses a solid region with volume equal to 5. Find the…

Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

A: Given F=(y-z)i+(z-x)j+(x+z)k S:r(r,θ)=(rcosθ)i+(rsinθ)j+(9-r2)k 0≤r≤3, o≤θ≤2π

Q: use the surface integral in Stokes’ Theorem to calculate the circulation of the field F around the…

Q: Verify Stokes Theorem for the vector field F(x, y, z) = (y-z)i + 3xy j + 5zk by evaluating the line…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

A: Given The given vector field is F=yi+xzj+x2k and the surface is 8x+y+z=8. Apply formula…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 2zi +…

Q: Use the surface integral in Stokes' Theorem to calculate the rotation of the field F = (y? + z?)i +…

Q: 14. Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field: (r…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F around the…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= zi+…

A: Calculate the flux of the curl of the field F = z i + 5 x j + y k, by using the surface integral in…

Q: Calculate the net outward flux of the vector field F = xy i + (sin xz + y2)j + (exy2 + x)k over the…

A: Given surface 'S' is surrounding region D bounded by the planes y=0, z=0, z=2-y and z=1-x2

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across…

Q: Use Stokes' Theorem to find the circulation of the vector field F =7xzi+(4x+5yz)j +5x^2k around the…

A: F=7xzi+(4x+5yz)j+5x2k,andcircle : x2+y2=1,z=4

Q: 3. Use the surface integral is Stokes' Theorem to calculate the flux of the curl of the field F…

Q: Verify Stokes’ Theorem for the vector field F = 2xyi + xj + ( y + z)k and surface z = 4 - x2 - y2,…

Q: Evaluate the flux integral ff. curl (z cos x i+yj+x sin y k) ds where S is the part of the outward…

Q: Let us verify Stokes' theorem using the vector field F = (x 2 - y)i + 4zj + x 2k, where the closed…

A: We are given a 3d vector field and a cloced conture, using which we have to justify the Stoke's…

Q: F =(-y,x,z) across the solid sphere E %3D

A: we have to find the outward flux

Q: use the surface integral in Stokes’ Theorem tocalculate the flux of the curl of the field F across…

Q: - For the vector field in the xy plane: F= (zi - v)), use Stokes theorem to compute the line…

A: We will use stokes theorem for 2d

Q: Use Stokes' Theorem to find the value of the line integral of the vector field F around the curve C…

Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: . Evaluate the flux integral f. curl (z cos xi+ yj+ x sin y k) dS where S is the part of the outward…

Q: . Consider the vector field F(r, y, z) = (8r sin y, 4x² cos y – e"z, –e" – sec² z). 1. Show that F…

Q: Compute the flux of the vector field F = xi + yj through the surface S, which is the part of the…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi +…

A: Given, F→=3yi^+5-3xj^+z2-2k^r→=3sinφcosθi^+3sinφsinθj^+3cosφk^ So, the flux of curl F is, Flux of…

Q: Find the flux of the curl of the vector field F(x, y, z) = [(z2 −4) cos(xyz), 3x+y,(z2 −4) sin(ex…

A: Surface is oriented outwards. And -2 <= z <= 2

Q: Apply Green’s theorem to find the outward flux for the field F =tan^−1?(y?/x)i+ln(x^2+y^2)j and…

Q: Find the flux of the field F = z k across the portion of the sphere x2 + y2 + z2 = a2 in the first…

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = by the…

Q: Verify Stokes' Theorem holds for the vector field F = yz i + x k where S is the portion of the plane…

A: The given vector field is F=yzi^+xk^ where S is the portion of the plane 3x+2y+6z=6 in the first…

Q: find the surface integral of the field F over the portion of the given surface in the specified…

Concept explainers

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length.

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.

Triple Integral

Examples:

Question

Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 5zi + xj + 2yk across the surface S: r(r,0) =r cos Oi +r sin 0j + (25 -) k, 0srs5, 0s0s2n in the direction away from the origin.
The flux of the curl of the field F is
(Type an exact answer, using n as needed.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Integration$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi + 5xj + 5yk across the surface S: r(r,0) =r cos ei +r sin ej + (9-r)k, 0srs3, 0s0<2n in the direction away from the origin. The flux of the curl of the field F is (Type an exact answer, using a as needed.)
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F= 5yi + (5 - 5x)j + (z² - 2)k S: r(), 0) = (V5 sin p cos e) i+ (V5 sin o sin 0) j+ (V5 cos 4) k, 0 spst/2,0s0s2a The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using t as needed.)
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 5yi + (5 - 2x)j + (z2 - 2)k S: r(ф, Ө) — (V10 sin o cos e)i+ (V10 sin o sin 0) j+ (V10 cos d) k, 0 < ¢p
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F = 3yi + (5 - 5x)j + (z² − 2)k S: r(0,0) = (√5 sin & cos 0) i + (√√5 sin þ sin 0)j + (√5 cos $) k, 0≤þ≤ñ/2, 0≤0≤2 The flux of the curl of the field F across the surface S in the direction of the outward unit normal n is (Type an exact answer, using as needed.)
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across the surface S in the direction away from the origin. F= 4yi + (5 - 5x)j + (z - 2)k S: r(), 0) = (V7 sin o cos 0) i+ (17 sin o sin 0) j+ (V7 cos o) k, 0
Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 2zi + 2xj + yk across the surface S: r(r,0) = r cos Oi +r sin 0j + Osrs3, 0<0< 2n in the direction away from the origin. (9-2) K, The flux of the curl of the field F is. (Type an exact answer, using t as needed.)
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 3₁ F = 2yi +5xj + z³k; C: the counterclockwise path around the perimeter of the triangle in the x-y plane formed from the x-axis, y- axis, and the line y = 5 - 6x
Find the curl of the vector field F = (3y cos(x), 4x sin(y)). curl F :
2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to