Integrate counterclockwise or as indicated. Show the details.
Integrate counterclockwise or as indicated. Show the details. cosh dz, C the boundary of the 2-Ti...
Show that integral dz/(z-1-i)n+1 =0, if n does not equal 0 and 2 pi i if n = 0 for C the boundary of the square 0<=x<=2, 0<=y<=2, taken counterclockwise. [Hint: Use the fact that contours can be deformed into simpler shapes (like a circle) as long as the integrand is analytic in the region between them. After picking a simpler contour, integrate using parametrization.]
6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the point (1, 0, 0) 6. (1 point) Use Stokes' Theorem to find the line integral /2y dx + dy + (4-3x) dz, where C is the boundary of the triangle with vertices (0,0,0), (1,3,-2), and -2,4,5), oriented counterclockwise as viewed from the...
Evaluate the integral $ 3z + 4)cos z dz, C:12+2i = 1 counterclockwise. z² +4 Integrate $c +436 yosz dz, C:/z+3–2i = 3 counterclockwise. (z +4)
Choose three questions to do The first method: the second method thank you 19-29 INTEGRATION Integrate by the first method or state why it does not apply and then use the second method. (Show the details of your work.) 19. | Re z dz, C the shortest path from 0 to 1 + i 20. J Re z dz, C the parabola y from 0 to 1 + i 21. | e2z dz, C the shortest path from Ti to...
Evaluate the integral 5. Ten dz, where C is the boundary of the square with vertices at the points 0, 1, 1+i and i, with a counter clockwise orientation. What is the integral over the reverse contour?
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.
2-1/2dz if C is a polygonal line with vertices 2,1 + i,-1 i,-2 (without the segment [-2,2) and z-1/ is a principal value. Hint: consider a particular branch which is analytic on the contour uate the following integrals (all contours are positively oriented): cosh(z) 3 dz if C is a square of vertices 1 ti,-1ti C 2 sin(2) dz if C is a circle 3 2(2,2 2 3 dz if C is a rectangle with sides along the lines x-1,x--1,y...
7. Evaluate SF. dr counterclockwise around the boundary C of the region D using Green's theorem: F = (x cosh 2y, 2x2 sinh 2y], D:? Sy <.
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...
Chapter 14, Section 14.1, Question 2S Integrate by the first method, if it applies, or use the second method. Im z2 dz, C counterclockwise around the triangle with vertices 0,4,4i. Enter the exact answer d), b * tan (a * θ) or e(a*x) * b Use an asterisk, * , to indicate multiplication. For example, 2 *f(x), a * x * (x + b) * (c * x ак