Compute the following:(a) Integrate the following vector field F = 2r cos(z)i + 2y cos(z)j − (r² + y²) sin(z)k overthe boundary of the hypocycloid shown below:Hypocycloid:=x2/3 + y2/3 - ²/3x = a cos³ (0)y = a sin³ (0)(b) Consider the following vector field F = x³yi+y sin(2)j-ryz³k. Compute V = V XF,and integrate the outward flux of the new vector field V through the spherical surfaceas defined by x² + y² + x² = 1.

(a) Line integral along a curve C. (b)~using Gauss Divergence theorem V is a volume bounded by a…

Compute the following: (a) Integrate the following vector field F = 2x cos(2)i + 2y cos(z)j — (x² + y²) sin(2)k over the boundary of the hypocycloid shown below: Hypocycloid: 2²/3 + y2/3 = ²/3 x = a cos³ (0) y = a sin³ (0) (b) Consider the following vector field F = r³yỉ+ y sin(2)j — ryz³k. Compute V = V ×F, and integrate the outward flux of the new vector field V through the spherical surface as defined by x² + y² + 2² = 1.

Compute the following: (a) Integrate the following vector field F = 2x cos(2)i + 2y cos(z)j — (x² + y²) sin(2)k over the boundary of the hypocycloid shown below: Hypocycloid: 2²/3 + y2/3 = ²/3 x = a cos³ (0) y = a sin³ (0) (b) Consider the following vector field F = r³yỉ+ y sin(2)j — ryz³k. Compute V = V ×F, and integrate the outward flux of the new vector field V through the spherical surface as defined by x² + y² + 2² = 1.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 16P

See similar textbooks