let F be the vector field (x,2x,)let C bethe bandary of the Surface S given by 4x?t y%LR?5877. Gven C the counter -clookwise orientation when vienadfrom Caboue) the postlive z anis. Evaluato theby ninga different surface boundedby Ca

We will use reverse of Stokes theorem for vector field F to convert given integral into line…

Answered: let F be the vector field Cx, 2x,3).…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Similar questions

Show that the regular surface S = {(x, y, z): x² + y² = z² + 1, x > 0 or y > 0} is orientable by constructing an example of a differentiable field of normal vectors N: S → S².
Let F be the vector field (x², 2r, 2²). Let C be the boundary of Lv **---- the surface S given by 4x? + y? + 2² = 5, z > 1. Give C the counter-clockwise orientation when viewed from (above) the positive z-axis. Evaluate the integral // (7 × F) - dš by using a different surface bounded by C.
Consider the vector fields below and the statements that follow: F, = (ze** +Azry, ye+ +8yz, 2). F2 = (6e" sin(y), 6e" cos(y), 422). i) Fi is conservative m) F2 is conservative. IS ) curl F2 is perpendicular to F2. iv) curl Fi is perpendicular to F1. v) curl Fi is perpendicular to F. Which one of the following is true? O Statements i) and ii) are true Statements i and iv) are true Statements ) and ivl and v) are true None of these options are true Statements iv) and v) are crue Only statement i is true
WHICH ANSWER IS CORRECT?
3. A vector field is given as F = â,2r² + âgr²Coso + âz5z. Verify Stokes theorem for this vector field using the surface defined by 1
Calculate line integral F. dr of conservative vector field F(x, y, z) from (-2,-5, 4) to (-3,7,-3). Enter an exact answer. A Provide your answer below: \displaystylefF.dr = 92² Y i- 9xz² y² j+ 18xz Y k, where A is a path
Show that on the saddle surface z= xy the two vector fields (V1+x* + V1+ y, yvl+x + xV1+ y*) are principal at each point. Check that they are orthogonal and tangent to M.
In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (X2+y²)k a. State whether F is conservative, and give a one-sentence justification for your statement b. Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation x=at, y=bt, z=ct (0sts1). c. Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.

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let F be the vector field Cx, 2x,3). let c be the of the Surface S gien by 4xt y1855 it. 871.Given c the conter -clooknise erientation when vienzd from Cabove) the poslive z ans. Evaluato the integ by usng a different surface bounded by C. .