2. More integrals! Evaluate each integral, using either a Cauchy Integral Formula or Cauchy's Residue Theorem....
4. (a) Use Cauchy's residue Theorem to provide alternative proofs for Cauchy's integral formula and its extension. (b) Evaluate z+ 4z + 5 dz, son z2 + z where C is the positively oriented circle of radius 2 centered at the origin.
5. Use Cauchy's residue theorem to evaluate the following integrals along the circle 121 = 4: C 22 5. Use Cauchy's residue theorem to evaluate the following integrals along the circle 121 = 4: C 22
using Cauchy's Residue Theorem and the so-alled pacman inte 6. (10 pts) Evaluate gration contour. using Cauchy's Residue Theorem and the so-alled pacman inte 6. (10 pts) Evaluate gration contour.
4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c) 4. Evaluate the following integrals using the Residue Theorem. Justify your calculations, show the work. (10 points each) a) 12 cos a + 13 2 da b) (x2 +6x + 10)2 x sin 2x 24 13 da: c)
Evaluate the integral. Does Cauchy's theorem apply? Show details . 2 & de 1 6 z dz > ¿ z2+ CZ til: i Z2+1 C: 12-11 Counterclockwile Counter clock wise
please 2 only, thanks Exercises dA (1) Use Cauchy's residue theorem to compute Jo 2+sin (2) Repeat the preceding exercise for 8" 131. (3) Let a be a complex number such that lal < 1. Prove that (2 27 Jo 1 - 2a cos 0 + a2d6 = 1 - 22 (4) What is the value of the integral in the preceding exercise when |al > 1? (Hint: Let b= 1.)
2. (3 pts.) Let C denote the unit circle, oriented clockwise. Evaluate the line integral ydx dy in two different ways: first by parameterizing the curve and using the definition of line integral; then, use Green's theorem. 2. (3 pts.) Let C denote the unit circle, oriented clockwise. Evaluate the line integral ydx dy in two different ways: first by parameterizing the curve and using the definition of line integral; then, use Green's theorem.
Use Green's theorem to evaluate the line integral S. (sin(22) – 5y) dx + (72 – y cos y) dy, where C is the the counter clockwise oriented closed curve consisting of the upper half of the circle (x – 5)2 + (y – 4)2 = 9 and the line segment between (2, 4) and (8,4).
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...
help with calc 3 hw 2. Use Green's Theorem to evaluate ScF.Tds, where C is the the circle of center (0,0) and radius 2 in the xy plane, oriented counter-clockwise, and F(x, y) = (x3, x). (Please give a numerical answer here. The integral is very easy.)