The circuit C, depicted below, is traversed clockwise starting and ending at -1. It consist of two parts: C = A + B whe...
need help with #4. need to identify best theorem to use and find solution. Table 14.4 Fundamental Theoremsdtb)-a) or Calculus Fundamental Theorem f.dr-un-nA) of Line Integrals Green's Theorem Circulation form) Stokes' Theorem F-nds Divergence Theorem Evaluate the line integral for the following problems over the given regions: 1. F (2xy,x2 C:r(t) (9-2.),0sts3 3X3dy-3y3dz; C is the circle of radius 4 centered at the origin with clockwise orientation. 2. 3. ye""ds; C is the path r(t) (t,3t,-6t), for Ost s In8...
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
Re -3 -2 -1 0 1 2 3 4 Note that C is not a simple curve, so Cauchy's integral formula does not directly apply. By breaking up C as needed, evaluate T z2+9 Jc (2+2-i)(2+1-i)z dz. Syntax notes: • When entering lists in the questions below, use commas to separate elements of the list. Order does not matter. • The complex number i is entered as I (capital i). z2+9 (a) The poles of (z+2-i)(2+1-i)z that lie inside Care...
2 +1 (b) Evaluate the contour integral dz, 22 – 9 where I is the boundary of the square D = {z E C:-4 < Re(z) < 4, -4 < Im(z) < 4} traversed once counterclockwise.
Question 10 (2 marks) Attempt 1 Use Green's theorem in the plane to evaluate anti-clockwise around the closed path C given by the curves: Evaluate the line integral as a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded to 10.13906 OR 3*Pi+5/7 KSkipped Question 10 (2 marks) Attempt 1 Use Green's theorem in the plane to evaluate anti-clockwise around...
we need to determine if the vector field depicted in graph 1 and graph 2 are conservative by using the last 3 bullets points in the picture Project 1. Fundamental theorem of line integrals In our course we learned the fundamental theorem of line integrals: if F is a conservative vector field with potential f and C is a curve connecting point A to b, then f-dr = f(B)-f(A). Moreover it happens if and only if for any closed curve...
solve 1 and 2. Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B) cos (x3) A) 6x5 cos (x3) Evaluate the integral. 3T/4 1) rt/4 D) o B)-16 C) Find the derivative of the integral using the Second Fundamental Theorem of Calculus 2) y- cos nt dt D) cos (3)-1 C) sin (3) B)...
Use Green's theorem in the plane to evaluate 4 K= anti-clockwise around the closed path C given by the curves: x-0, -1 2 y 2 -2 r 2, -TT/2 <0< T/2, x = 0, 2 2 yz 1, r= 1, TT/2 2 0 2 -T/2 Evaluate the line integral ass a double integral using polar coordinates. Your answer should consist of a single number accurate to five decimal digits or as an exact rational expression. For example: 10.13906368 OR rounded...
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II curve ll surface is: and: Divergence Theorem The vector field |l curve l surface is: (b) For each of the following, choose all correct answers from the list below that can be used to evaluate the given integral. List items may be used more than once. i....