please solve +y-1. 15.) Evaluate: F dr, where F(x, y) = xyi +(y+ x) j and C is the unit circle +y-1. 15.) Evaluate...
4. (8E given: F(x,y)- xyi-y'i Evaluate Jr where C is represented by ) as
Use (part A) line integral directly then use (part B) Stokes' Theorem 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C is the unit circle in the plane z (a) 67 (d) 12m 3. (b) TT (e) None of these (c) 3 TT 10. Use Stokes's Theorem to evaluate F dr where F(x, y, z) (3z 2y)i + (4x 3y)j + (z + 2y)k and C...
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1 For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1
Chapter 15, Section 15.8, Question 007 Use Stokes' Theorem to evaluate F dr F(x, y,z)3i 10x j+ 8y k where is the boundary of the paraboloid shown in the figure below. Chapter 15, Section 15.8, Question 007 Use Stokes' Theorem to evaluate F dr F(x, y,z)3i 10x j+ 8y k where is the boundary of the paraboloid shown in the figure below.
(1 point) Suppose F(x, y) = xyi + (x – y)j and C is the triangle from (4,0) to (-4,0) to (0,4) to (4,0). (a) Find the line integral of Ể along each segment of the triangle. Along C1, the line segment from (4,0) to (-4,0), the line integral is Along C2, the line segment from (-4,0) to (0,4), the line integral is Along C3, the line segment from (0,4) to (4,0), the line integral is (b) Find the circulation...
Evaluate line integral ( F. dr where C is any positively oriented simple closed curve that encloses the origin by using a circle of radius r, and r is small enough so that the circle lies entirely inside C given F(x, y) = ? 1)_ 2xyi +(y2 – xº)j Ans (x² + y²)
Evaluate the integral ∮CF⋅dr for F=(5x2y)i+(2x2−5xy2)j on the curve C consisting of the x-axis from x=0 to x=3, the arc of the circle x2+y2=9 up to the line y=x, and the line y=xdown to the origin. ∮CF⋅dr= Evaluate the integral h. F . dr for F = (5x2 y)i + (2x2-5yj on the curve C consisting of the x-axis from x=0 tox-3, the arc of the circle x2 + y2-9 up to the line y=x, and the line y=xdown to...
10. Use Green's theorem to find f dr where 1 F(x,y) -2,23, อี่+ry2 and C is the circle 2,2 +Y'2 4 oriented counterclockwise. 10. Use Green's theorem to find f dr where 1 F(x,y) -2,23, อี่+ry2 and C is the circle 2,2 +Y'2 4 oriented counterclockwise.
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).
15. Let F(z,y)- F dr where C is any positively-oriented Jordan curve that encloses the origin Evaluate 15. Let F(z,y)- F dr where C is any positively-oriented Jordan curve that encloses the origin Evaluate