Let M be the capped cylindrical surfacewhich is the union of two surfaces, a cylindergiven by x² + y² = 9, 0 ≤ z < 1, and ahemispherical cap defined byx² + y² + (z − 1)² = 9, z ≥ 1. For thevector fieldF=(x²),: (zx + z²y +2y, z³yx + 4x, z²x²compute M (V × F) · dS in any way youlike.ſſ₁(▼ × F) · dS=•

Step 1: Step 2: Step 3: Step 4:

Answered: Let M be the capped cylindrical surface…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

3. Find a vector function that represents the curve of intersection of the paraboloid z = r+y and the cylinder r+y = 16.
11. If F= (y² + z? – x³) î + (z² + x² – y³)j+(x² + y² – z³) k, evaluate fcurl F-î ds integrated over the portion of the surface x + y – 2ax + az = 0 above the plane z = 0 and verify Stoke's Theorem; where n is unit vector normal to the surface. (4.M.I.E.T.E., Winter 20002) Ans. 2 n a
Evaluate 1 x² + y² + z² between the spheres x² + y² + 2² = 9 and x² + y² + z² = 36 in the first octant. JSS₂ ² dV, where E lies
b) The line integral F. dr is a scalar.
- Parametrize the intersection of the surfaces y² = z² = x − 1, y² + z² are needed). (Use symbolic notation and fractions where needed.) x(t): = y(t) = = z(t) = ± = 25 using t = y as the parameter (two vector functions
Use the Divergence Theorem to evaluate (4x + 3y + z2) ds Is where S is the sphere x2 + y2 + z2 = 1.
4. a) Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the plane z = 1. b) Let S be the surface parametrized by x = u + 3; y = v + 2; z = uv². Show that the point P with (x,y,z) co-ordinates (4,4,4) lies on S and find an equation of the tangent plane to S at point P.
Let F = (z, 0, y) and let S be the oriented surface parametrized by Þ(u, v) = (u² – v, u, v²) for 0 ≤ u ≤ 3, −1 ≤ v ≤ 4. (a) Calculate N and F. N as functions of u and v. (Use symbolic notation and fractions where needed.) N = (2v,-4uv,1) F.N= (b) Calculate the normal component of F to the surface at P = (6,3,9) = Þ(3, 3). (Use symbolic notation and fractions where needed.) normal component at P = Incorrect 2v³+u IF (c) Calculate F. ds. (Give your answer as a whole number.) F.dS= 63 1333 Incorrect

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS