PLease simplify your answer at the end and make sure they are not still in integral.
Doubt or problem in this then comment below.. i will help you..
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please thumbs up for this solution..thanks..
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PLease simplify your answer at the end and make sure they are not still in integral....
Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 5yzi + 9x j +2yze+'k ,S is the portion of the paraboloid z = x2 + aby2 for 0 sz s 3, and the unit normal on S points away from the z-axis. 16 Enter your answer symbolically, as in these examples
Problem #9: Use Stokes' Theorem (in reverse) to evaluate Sf (curl F). n ds where F = 7yzi + 9x j +6yzet k ,S is the portion of the paraboloid z = 36 x? normal on S points away from the z-axis. + for 0 sz s 4, and the unit 64. -3648*pi Enter your answer symbolically, as in these examples Problem #9: -36481 Just Save Submit Problem #9 for Grading Problem #9 Attempt #1 Attempt #2 Attempt #3 Attempt...
Problem #2: Д eн (curl F) n dS where Use Stokes' Theorem (in reverse) to evaluate 10yze normal on S points away from the z-axis k ,S is the portion of the paraboloid 7yzi Зxј F for 0 s z s 2, and the unit + Z = 16 + 64 = Enter your answer symbolically, as in these examples Problem #2: Just Save Submit Problem #2 for Grading Attempt #3 Attempt #4 Problem #2 Attempt 1 Attempt #2 Attempt...
. Problem #8: Use Stokes' Theorem to evaluate | F• dr where F = (x + 52)i + (6x + y)j + (7y - -)k and C is the curve of intersection of the plane x + 3y += = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) Problem #8: Just Save Submit Problem #8 for Grading Attempt #1 Attempt #2 Attempt #3 Attempt #4 Attempt #5 Problem #8 Your Answer: Your Mark:...
I will rate your answer so please make sure the answer is accurate. The following question is a Calculus 3 problem, please answer 2) in the picture shown below, please show all the steps (step by step) and write out nicely and clearly: 1. Use Stokes, Theorem to find ls (curlF): ndS where F(x, y, z) = (y2z,zz, x2y2) and s is the portion of the paraboloid z x2 + y2 that lies inside the cylinder x2 +y-1. Use the...
Please show full working. Only answer if you know how. Regards (2) Let F-~itrj yk and consider the integral JTs ▽ x F·ń dS where s is the surface of the paraboloid z = 1-2.2-y2 corresponding to z > 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. (b) Evaluate the integral directly over the surface S (c) Evaluate the integral directly over the new surface S...
(2) Let F-1 + rj + yk and consider the integral- , ▽ × F. т. dS where s is the surface of the paraboloid z = 1-12-y2 corresponding to z 0, and n is a unit normal vector to S in the positive z-direction (a) Apply Stokes' theorem to evaluate the integral. (b) Evaluate the integral directly over the surface S rectlv over the new surface (2) Let F-1 + rj + yk and consider the integral- , ▽...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
= and z= 8. Let A be the part of the cylinder x2 + y2 1 between the planes z = 2, where n points away from the z-axis. Let C be the counterclockwise boundary of A. Let F(x, y, z) = (2xz + 2yz, –2xz, x2 + y²). Verify Stokes' Theorem: (a) Evaluate the line integral in Stokes' Theorem. (Hint: C has two separate parts.] (b) Evaluate the surface integral in Stokes' Theorem. Hint: curl (F) = (2x +...
Verify Stokes' Theorem by evaluating the line integral and the double surface integral. Assume that the surface has an upward orientation. (a) F(x, y, z)= x’i + y²j+z?k; o is the portion of the cone below the plane z=l. (b) 7 (x, y, z)=(z - y){ +(z+x) ș- (x + y)k; o is the portion of the paraboloid z=9-r? - y2 above the xy-plane. [0, 187]