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1. Compute each of the following integrals using a technique of your choice. Then for each...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly,...
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...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axi...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
1. Let F-yi(xr +6g) j + 2z k and (a) Which of these two fields (if any) are conservative on R3? Give detailed (b) Find potential functions for the fields that are conservative (c) Calculate the line...
1. Let F-yi(xr +6g) j + 2z k and (a) Which of these two fields (if any) are conservative on R3? Give detailed (b) Find potential functions for the fields that are conservative (c) Calculate the line integrals F dr and G dr where C is the arc of the reasoning r2 4 curve formed by the intersection of the plane z = 4 and the surface--+92 in the first octant, oriented anti-clockwise when view from above.
1. Let F-yi(xr...
please respond with explanations for each step. thank you Problem 4 Evaluate the line integrals (a) (10 points) y da...
please respond with explanations for each step. thank
you
Problem 4 Evaluate the line integrals (a) (10 points) y da 2ax dy, where C is the curve r(t) (2t + 1) i+ 3t2 j, 0t 1. (b) (10 points) (ryz) ds, where C is the line segment from the point (2, 1,0) to the point (4,3,6) (c) (10 points) F.dr,where F is the vector field F(x, y) = yi - rj and C is the curve given by r(t) t2i+...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first oc...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
4. (10 points, 5 points each) Multiple choice: i. Which one of the following integrals is...
4. (10 points, 5 points each) Multiple choice: i. Which one of the following integrals is NOT equivalent to the rest? f(x,y,z) dx dy dz √1–y² f(x,y,z) dx dz dy -√1-y? (a) [ L. (b) LIM SIN (a) [, [['f(x,y,z) dz dx dy (c) f(x,y,z) dy dx dz (e) These are all different M ii. Which of the following gives a parametrization for a straight line that passes through the points (-1,0) and (1,4)? (a) r(t) = (-1+t, 4t) where...
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in the counterclockwise direction n is the outward-...
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in the counterclockwise direction n is the outward-pointing normal vector on , and C is the boundary (b) (15 points) Evaluate directly the line integral p F- nds in part (a).
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
1. Evaluate the surface Integrals using Divergence (Gauss') Theorem. a) ff(xyi +2k)ndS where S is...
1. Evaluate the surface Integrals using Divergence (Gauss') Theorem. a) ff(xyi +2k)ndS where S is the surface enclosing the volume in the first octant bounded by the planes z-O, y-x, y-2x, x + y+1-6 and n İs the unit outer normal to S. b) sffex.y,22)idS, where S is the surface bounding the volume defined by the surfaces z-2x2 +y, y +x2-3, z-0 and n İs the unit outer normal to S. o_ ffyi+y'j+zykids, where S is the ellipsoid.x^+-1 and iis...
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...
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...
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...
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
Find J, F-T ds where F(x, y, z) of the cylinder (Vz3 + уз + 5, z,z") and is the intersection with the plane ((-1, y.a)) oriented in the clockwise direction when viewed from the positive x-axis.
1. Let F-yi(xr +6g) j + 2z k and (a) Which of these two fields (if any) are conservative on R3? Give detailed (b) Find potential functions for the fields that are conservative (c) Calculate the line integrals F dr and G dr where C is the arc of the reasoning r2 4 curve formed by the intersection of the plane z = 4 and the surface--+92 in the first octant, oriented anti-clockwise when view from above.
1. Let F-yi(xr...
please respond with explanations for each step. thank
you
Problem 4 Evaluate the line integrals (a) (10 points) y da 2ax dy, where C is the curve r(t) (2t + 1) i+ 3t2 j, 0t 1. (b) (10 points) (ryz) ds, where C is the line segment from the point (2, 1,0) to the point (4,3,6) (c) (10 points) F.dr,where F is the vector field F(x, y) = yi - rj and C is the curve given by r(t) t2i+...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
4. (10 points, 5 points each) Multiple choice: i. Which one of the following integrals is NOT equivalent to the rest? f(x,y,z) dx dy dz √1–y² f(x,y,z) dx dz dy -√1-y? (a) [ L. (b) LIM SIN (a) [, [['f(x,y,z) dz dx dy (c) f(x,y,z) dy dx dz (e) These are all different M ii. Which of the following gives a parametrization for a straight line that passes through the points (-1,0) and (1,4)? (a) r(t) = (-1+t, 4t) where...
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in the counterclockwise direction n is the outward-pointing normal vector on , and C is the boundary (b) (15 points) Evaluate directly the line integral p F- nds in part (a).
(a) (15 F-(1+9) 9. points) Apply Green's theorem to evaluate φ F.nds, where (x2 +y)j, of a triangle with vertices (1,0), (0,1). (-1,0) oriented in...
1. (2 points) Find F dF if curl(F) 3 in the region defined by the 4 curves and C4 Ci F . d7 where F(x,y,z)-Wi +pz? + Vi> and C consists of the arc of the 2. (2 points) Evaluate curve y = sin(x) from (0,0) to (π, 0) and the line segment from (π,0) to (0,0). 4 3 3. (2 points) Evaluate F di where F.y,(ry, 2:,3) and C is the curve of intersection of 5 and y29. going...
1. Evaluate the surface Integrals using Divergence (Gauss') Theorem. a) ff(xyi +2k)ndS where S is the surface enclosing the volume in the first octant bounded by the planes z-O, y-x, y-2x, x + y+1-6 and n İs the unit outer normal to S. b) sffex.y,22)idS, where S is the surface bounding the volume defined by the surfaces z-2x2 +y, y +x2-3, z-0 and n İs the unit outer normal to S. o_ ffyi+y'j+zykids, where S is the ellipsoid.x^+-1 and iis...
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...
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