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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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
Evaluate of the infsont of the Yz-plant S plane x fytz =1 that ies
Compute foF-dr, where C' is the oriented curve in the figure to the right, and F is the vector field below. F(x, y): if y < 2 (3x-yx)i + (y-2) j if y ≥ 2 ri 4 3 2 1 P e S 1 2 R 3 Q 8
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
. Sketch the following two balls in the given vector space, with usual norm: (а) В-(—1,1) E R? (b) В,(-1, 2, 1) ERY. . In R' with the usual norm, show that (2, 1, –1) e B2(-1,0,0).
Let F =. Compute the flux of curl(F) through the surface z = 1- x² - y² for x² + y² ≤ 11 oriented with an upward-pointing normal. Flux = help (fractions) (Use symbolic notation and fractions where needed.) Hint: Stokes' Theorem shows a direct computation can be done in an alternative fashion.
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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. .