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8, (5 points) Set up, but do not integrate, the line integral of the vector field...
Problem 3. Vector Calculus (30 points) Set up the equations for Stoke's theorem for the vector...
Problem 3. Vector Calculus (30 points) Set up the equations for Stoke's theorem for the vector field B frcosd + psinp in the surface shown below. No need to evaluate the equations (a) Write the closed contour integral equation and simplify any vector algebra (gradient, divergence, curl, dot product, etc.). Do not evaluate the integral. (15 points) (b) Write the open surface integral equation and simplify any vector algebra (gradient, divergence, curl, dot product, etc.). Do not evaluate the integral....
13. (5 points) Reverse the order of integration for the following iterated integral. You do not...
13. (5 points) Reverse the order of integration for the following iterated integral. You do not have to integrate. cos y dy dx 14. (5 points) Integrate the function g(r,0) = p sin over the sector of a disc in the first quadrant bounded by the circle r² + y2 = 1, the circle r² + y2 = 4, the line y = rV3, and the r-axis. 15. (5 points) Convert the following iterated integral from Cartesian to polar. You...
using stokes theorem, set up integral that will calculate the circulationof the vector field Use Stokes'...
using stokes theorem, set up integral that will calculate the
circulationof the vector field
Use Stokes' Theorem to find the integral which will calculate the circulation of the field F(x, y, z) = yzi + xzj + xyk where C is the intersection of the cylinder x + z2 = 9 and the planes z = 0, y = 0 and y = 1. Do not evaluate this integral.
1. Set up, but do not evaluate, an integral to find the area enclosed by the...
1. Set up, but do not evaluate, an integral to find the area enclosed by the x-axis and the [x = 1 + et curve ly = t-t2 2. {*5+?2t Osts2 y = VE (1) Find the equation of the tangent line at the point where t = (2) Set up, but do NOT evaluate, an integral to find the area of the surface obtained by rotating the curve about the y-axis. 3. Set up but do NOT evaluate an...
This Test: 18 pts possible 5 of 18 (1 comnplete) the foillowing vector field and region. Check for agreement Evaluat...
This Test: 18 pts possible 5 of 18 (1 comnplete) the foillowing vector field and region. Check for agreement Evaluate both integrals of the Divergence Theorem D= (xy.z): x2 + y2 + 22 s9) F (4x,3y,32); the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice. Set up the volume integral OA !!! dp do d8, where the integrand does not simplity to a constant 0 0 O B. The integral simplifies to...
show works please Q4 10 Points In a Set up, but do NOT solve, the integral...
show works please
Q4 10 Points In a Set up, but do NOT solve, the integral that will give the exact length of the curve x2 y from x = 1 to x = 2. Show all 2 4 your work.
(a) Set up a double integral for calculating the flux of the vector field F(x, y,...
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk...
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line...
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line...
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
Problem 3. Vector Calculus (30 points) Set up the equations for Stoke's theorem for the vector field B frcosd + psinp in the surface shown below. No need to evaluate the equations (a) Write the closed contour integral equation and simplify any vector algebra (gradient, divergence, curl, dot product, etc.). Do not evaluate the integral. (15 points) (b) Write the open surface integral equation and simplify any vector algebra (gradient, divergence, curl, dot product, etc.). Do not evaluate the integral....
13. (5 points) Reverse the order of integration for the following iterated integral. You do not have to integrate. cos y dy dx 14. (5 points) Integrate the function g(r,0) = p sin over the sector of a disc in the first quadrant bounded by the circle r² + y2 = 1, the circle r² + y2 = 4, the line y = rV3, and the r-axis. 15. (5 points) Convert the following iterated integral from Cartesian to polar. You...
using stokes theorem, set up integral that will calculate the
circulationof the vector field
Use Stokes' Theorem to find the integral which will calculate the circulation of the field F(x, y, z) = yzi + xzj + xyk where C is the intersection of the cylinder x + z2 = 9 and the planes z = 0, y = 0 and y = 1. Do not evaluate this integral.
1. Set up, but do not evaluate, an integral to find the area enclosed by the x-axis and the [x = 1 + et curve ly = t-t2 2. {*5+?2t Osts2 y = VE (1) Find the equation of the tangent line at the point where t = (2) Set up, but do NOT evaluate, an integral to find the area of the surface obtained by rotating the curve about the y-axis. 3. Set up but do NOT evaluate an...
This Test: 18 pts possible 5 of 18 (1 comnplete) the foillowing vector field and region. Check for agreement Evaluate both integrals of the Divergence Theorem D= (xy.z): x2 + y2 + 22 s9) F (4x,3y,32); the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice. Set up the volume integral OA !!! dp do d8, where the integrand does not simplity to a constant 0 0 O B. The integral simplifies to...
show works please
Q4 10 Points In a Set up, but do NOT solve, the integral that will give the exact length of the curve x2 y from x = 1 to x = 2. Show all 2 4 your work.
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
Line Integral & Path Independency Problem 1 Prove that the vector field = (2x-3yz)i +(2-3x-2) 1-6xyzk is the gradient of a scalar function f(x,y,z). Hint: find the curl of F, is it a zero vector? Integrate and find f(x,y,z), called a potential, like from potential energy? Show all your work, Then, use f(x,y,z) to compute the line integral, or work of the force F: Work of F= di from A:(-1,0, 2) to B:(3,-4,0) along any curve that goes from A...
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
Math 2177 4) For vector field f(x, y) = (xy, 2-y): i set up the line integral along the following paranie trized curves. G: gradient of any function f(x, y). Horizontal E vertical - Ellipse (9,14) (7,11) (13,7) ii) show that f(x, y) is not equal to the C, (579)
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