

Please show work and explain.
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Please show work and explain. Thank you. I rate correct work! Use either Stokes' theorem or...
Use either Stokes' theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way 17. Derive the following vector integral theorems volume τ surface inclosing T Hint: In the divergence theorem (10.17), substitute V-dC, where C is an arbitrary constant vector, to obtain C. J. ф dT c. fond. Since C is arbitrary, let C- i to show that the r components of the two integrals are equal; similarly, let C-j and C -k...
Question 39
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For the following integral, say whether Stokes' Theorem, the Divergence Theorem, or neither applies: ſcuri(2xî + zſ+2y3k).DĀ, 's where S is a triangular plane in space oriented downward. Stokes' Theorem O Divergence Theorem Neither Question 40 Calculate curl H, where H = 9xi - 8xyj + xzk. A) 259 - Byk B) -25j - Byk C) 25î - Byk D) -25j + 8yK
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Page 1 10. Use Stokes Theorem to evaluate S. curl F. ds F = (x, y, z) = z² i + 2xj + y2k, S:z = 1 - x2 - y2, z 20
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(2) Use Stokes' Theorem to evaluate the integral F.dr, where F(x, y, z) =< -Y, I, z > and where S is the upper hemispherical surface defined by z = v1- 2 - y2. The boundary of S is the curve C defined by Cos (t) y= sin (t) 0t 27 Z=0
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Use Stokes' Theorem to evaluate Sc F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = xyl +22+ 4yk, C is the curve of intersection of the plane X + 2 = 10 and the cylinder x2 + y2 - 36.
Show all work and use correct notation for full credit. Stokes' Theorem: Let S be an orientable, piecewise smooth surface, bounded by a simple closed piecewise smooth curve C with positive orientation. Let F be a vector field with component functions that have continuous partial derivatives on an open region in R3 that contains S. Then | | curl(F) . ds F-dr = where curl(F) = ▽ × F. (2 Credits) Let S be the cone given by {(z, y,...
USE GREEN'S THEOREM PLEASE THANK YOU
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Please show this by applying/using Green's theorem
3.] Show that the area enclosed by a counterclockwise curve C in the plane is given by Verify the formula works for the triangle with vertices (1,0), (0,2), (-1,0)
Evaluate the following integrals:
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5. [ 17+4?)" 67 -12 d. sec(Inx) tan(Inx) a. X b. Ja tu ar c. sin(2t)dt
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Exercise 2.5. Use the Binomial Theorem to prove that, for all n 20 and for all x e R, Hint: Set y 1 in Theorem 2.2.8 and then differentiate. Exercise 2.6. Use the result of the previous exercise to find the value of the sum + 2 + 10 10
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A hemisphere S is defined by x2 +y2+z2=4 on z20. A vector field F =2yi* -xj” +xzkº exists over the surface and around its boundary C. Use Stokes' Theorem to calculate SSs curlF. NºdS.