8 points each 1. F is a conservative vector field. Evaluate ScF. dr where F =< 2xy3-4, 3x2y224, 4x^y323 > and C is the curve beginning at (3, 0, 5) and ending at (3, 2, -1)
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
Evaluate the following integrals...
(1 point) Evaluate the following: a. 1 (8 + e-t) $(t – 4) dt = J-1 (6 | (8 + e +) 8(t – 7) dt = . %8+*80) dr = (8 + e +) 8(t) dt = 00
5. Evaluate the integral sec" x dr. 6. Evaluate the integral I 2 dx X3 V x2 – 1 >1. 7. Evaluate the integral dc I VAI 8. Evaluate the integral 19 - 22 dc. .x2
COS Use a contour to evaluate dr (2° +1)
(1 point) Use Stokes' Theorem to evaluate / (2xyi + zj+ 3yk) dr where C is the intersection of the plane x z 8 and the cylinder x2 y9oriented counterclockwise as viewed from above. Since the ellipse is oriented counterclockwise as viewed from above the surface we attach is oriented upwards curl(2xyi+zj +3yk)- 2,0,-2x The easiest surface to attach to this curve is the interior of the cylinder that lies on the plane x + z-8. Using this surface in...
1. Evaluate the following: (4 points) Sr* +23 dr
please describe ur answer
7. (8 points each) Evaluate the following. (a) dr. (b) lim 7-10 In(10.12 +2+1) 2.1 sin's coser 8. (9 points) Find the solution of cos I)} = (sin I Cosz)y if y(0) = 1.
dr J0 3. Let a be a positive constant such that a 1. Evaluate the definite integral using the technique in complex analysis, -C 27 dar I 1+a2 2a cos(1) Jo (a) State a precise version of Beu 4.
dr J0 3. Let a be a positive constant such that a 1. Evaluate the definite integral using the technique in complex analysis, -C 27 dar I 1+a2 2a cos(1) Jo (a) State a precise version of Beu 4.
Problem #8: Use Stokes' Theorem to evaluate F. dr where F = (x + 5z) i + (6x + y)j + (9y – =) k and C is the curve of JC intersection of the plane x + 2y += = 8 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) Problem #8: