1.Evaluate the surface integral2² +2²doYwhere S is the surface represented by r(u, v) = (2 cos v, u, 2 sin v), 1 ≤u ≤ 3, 0≤ v ≤ 2.S

Note: When r→(u,v)=< x(u,v), y(u,v), z(u,v)>, then dσ=||ru→ x rv→||dudv

Answered: Evaluate the surface integral x² +22…

Evaluate the surface integral x² +22 11,²² y where S is the surface represented by r(u, v) = (2 cos v, u, 2 sin v), 1 ≤u≤ 3, 0≤v ≤ 2. do

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

See similar textbooks

Related questions

Q: . A donut with major radius R and minor radius r can be represented parametrically by r(u, v) =…

Q: find the angles between the curves v=u2, v=u3, lying on the surface x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

Q: 2) Find the area of the surface r(u,v)=u cos vi+u sin vj+2vk where 0su<3 and 0<vs 2n .

Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Determine the area of the parametric surface S with equation R(u, v) = (u²+v², 2uv, u²_v²) where 0 ≤…

Q: Let F 8x'i + 8y³j + 8z°k. Evaluate the surface integral of F over the unit sphere.

Q: Let S be the surface parametrized by R(u, v) = (2u sin v, 2u cos v, -v), where 0 ≤ u ≤ 2 and 0 ≤ ≤.…

Question

1.
Evaluate the surface integral
2² +2²
do
Y
where S is the surface represented by r(u, v) = (2 cos v, u, 2 sin v), 1 ≤u ≤ 3, 0≤ v ≤ 2.
S

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
Sketch and describe, in your own words, the surface S parametrized as follows: ř (u, v) = (3 cos v, u, 3 sin v), 0≤u ≤ 8, 0 ≤ v ≤ 2n.
3. A donut with major radius R and minor radius r can be represented parametrically by r(u, v) = ((R+r cos u) cos v, (R+r cos u) sin v, r sin u) for 0 ≤ u ≤ 27 and 0 ≤ v ≤ 2π. What is the surface area of the donut?
Let S be the surface parametrized by R(u, v) = (2u sin v, 2u cos v, -v), where 0 ≤ u ≤ 2 and 0 ≤ ≤. Evaluate f4yz² do. S
Draw the parameterized surface. (Decide on a reasonable domain for u and v.)
If a parametric surface given by r₁(u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -4 ≤ u ≤ 4,-2 ≤ v ≤ 2, has surface area equal to 8, what is the surface area of the parametric surface given by r2(u, v) = 5r₁(u, v) with −4 ≤ u ≤ 4, −2 ≤ v ≤ 2? 27
Ex.5. Find a surface satisfying the equation p?z = 6x+ 2 and touching z = x' + y along its etion by the plane x + y + 1 = 0. Ans. z =x +y + (x + y + 1)
Given F=yi-zj+0k and parametric surface (u,v) = ui + v²j+(u-v) for 0
2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane at (2, 5, 1) in terms of (u, v) as well as in terms of (x, y, z).
7. Consider the surface S defined by the equation x3 +y2 – 3x - 2y – 4z = -2. Find all points P = (x, y, z) so that the vector v = (-18,4,8) is normal to the tangent plane to S at P. %3D
Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x2 + xy + 1.
9. Let S be the surface parametrized by (u, v³, u + v) where 0