Work In Exercises 25-28, use Green’s Theorem to calculate the work done by the force F on a particle that is moving counterclockwise around the closed path C.
C: boundary of the region lying between the graphs of
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CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
- Evaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis. Circulation = Prevs So F.dr-arrow_forwardLet F(x,y,z) = (-xy, x, 0) and let C be the curve of intersection of the plane x+y+z=1 and the cylinder x² + y² = 1, oriented counterclockwise when viewed from above. (a) Sketch the surfaces and highlight the curve of intersection C. (b) Parametrize the curve C. (c) Evaluate f. F. dr using the definition; that is f F · dr = ſ'° F (F(t)) · F¹' (t)dt. (d) Compute the curl of F. (e) Use Stokes' theorem to compute fF.dr. You should get the same result as in (c).arrow_forwardLet 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.arrow_forward
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