Chapter 10.9 Problem 9. Stokes's Theorem. Evaluate the line integral For'ds by Stokes's theorem, clockwise as...
Verify Stokes's Theorem by evaluating F-T ds = For as a line integral and as a double integral F(x, y, z) - (-y+z)i + (x - 2)j + (x - y)k S: Z - 16 - x2 - y220 line integral double Integral I Need Help? Read it Watch Talk to a Tutor
Use Stokes's Theorem to evaluate F dr. In this case, C is oriented counterclockwise as viewed from above. S: the first-octant portion of x2 + z2 -64 over x2 + y2-64
Use Stokes's Theorem to evaluate F dr. In this case, C is oriented counterclockwise as viewed from above. S: the first-octant portion of x2 + z2 -64 over x2 + y2-64
4.Use Green's Theorem to evaluate the line integral. ∫C 2xydx + (x + y)dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x2_______ 5.Use Green's Theorem to evaluate the line integral. ∫C ex cos(2y) dx - 2ex sin(2y) dy C: x2 + y2 = a2 _______
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...
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
Problem 4: Use the surface integral in Stokes' theorem to evaluate F.dr for the hemisphere S : x2 + y2 + z2 = 9; z > 0, its bounding circle C: 2+9 and the field F-yi- xj. You only have to compute the surface integral, not the line integral. (20 points)
Use Green's Theorem to evaluate the line integral. (x - 97) dx + (x + y) dy C: boundary of the region lying between the graphs of x2 + y2 = 1 and x2 + y2 = 81 x-9
Use Green's theorem to evaluate line integral F.dr, where F(x, y) = (y2 – x2)i + (x2 + y2)j, and C is a triangle bounded by y = 0, x = 6, and y = x, oriented counterclockwise.
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...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...