(a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric equations x = au cos(v), y = bu sin(v), z = u², 0sus 2, 0svs 2n. 27 O A(S) = V 4b?u* cos?(v) + 4a²uª sin²(v) + a²b?u² du dv r 27 (2bu? cos(v) + 2au² sin²(v) + abu) du dv O A(S) = r 2n O A(S) = V 4b?u* cos(v) + 4a²uª sin(v) + a²b?u² du dv O A(S) = || (2bu² + 2au? + abu) du dv O A(S) = V 4b?uª + 4a²uª + a²b?u² du dv

(a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric equations x = au cos(v), y = bu sin(v), z = u², 0sus 2, 0svs 2n. 27 O A(S) = V 4b?u* cos?(v) + 4a²uª sin²(v) + a²b?u² du dv r 27 (2bu? cos(v) + 2au² sin²(v) + abu) du dv O A(S) = r 2n O A(S) = V 4b?u* cos(v) + 4a²uª sin(v) + a²b?u² du dv O A(S) = || (2bu² + 2au? + abu) du dv O A(S) = V 4b?uª + 4a²uª + a²b?u² du dv

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

Related questions

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

Q: x(t) = 3 cos t y(t) = 8 sin t 0<t< 2n a) What does the curve described by these parametric equations…

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

Q: Use hyperbolic functions to parametrize the intersection of the surfaces x² - y2 = 25 and z = 5xy.…

A: Surfaces : ,

Q: dy dy and dx 1) Parametric equations given below. Find are dx2 x = t+ In t, y = t² + 1

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

Q: Given x = 2 cost + 38 and y = 5 sin2t %3D

Q: 254. Find the distance between point A(4, 2, 5) and the line of parametric equations x=-1-t, y=-t, z…

A: The given parametric equation is x=-1-t, y=-t, z=2, t∈ℝ and the point is A4,2,5. Find the distance…

Q: A parametric curve C is given by the position vector F(1)=sin(21). sin" (+),e' osis Osis". a) Find…

A: a)The given position vector is, r→(t)=12sin(2t),sin2t,et

Q: Solve the following differential equation. Use UC method for the nonhomogenous solution: d²y dy +…

Q: a) Find the equation of tangent line of curve that is given by parametric equations X = 3cost + sint…

A: (a) Given parametric form of curve is…

Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: Parametrize the intersection of the surfaces y² - z² = x - 1, y² + z² = 36 using trigonometric…

Q: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

Q: Calculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to…

Q: . Find a cartesian equation for the given parametric equations: a) x = t2 – 4 and y =t+1 b) x = 2…

A: Eliminating t

Q: The ancient Japanese hand fan pictured below is described parametrically by *(u, v) = (v² cos(u), v²…

Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

Q: Consider the parametric curve C given by X= St. y = 5 sin²t where te [0.2] (₁) Determine the values…

Q: x = 3 sin(t), y = cos(t 2 urve of intersection of the surfaces z = x² an

A: Perametric equation .

Q: Use one of the formulas in (5) to find the area under one arch of the cycloid x = t - sint and y =…

Question

(a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric equations x = au cos(v), y = bu sin(v), z = u?, 0 <u< 2, 0< v < 2n.
O A(S) =
V 4b?u4 cos?(v) + 4a?u4 sin?(v) + a²b?u² du dv
2n
O A(S) =
(2bu? cos(v) + 2au? sin?(v) + abu) du dv
27
O A(S) =
T V4b?ut cos(v) + 4a²ut sin(v) + a?b?u? du dv
s (2bu? +
O A(S) =
2au?
+ abu) du dv
27
2
O A(S) =
V 4b?u4 + 4a²u4 + a?b?u² du dv
(b) For the case a = 2, b = 3, and for the constant vector field F(x,y,z) = 3i + k, find the flux of F through the surface S.
F-ds equals

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Triple Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Question The position of a drone at time t≥ 0 (in minutes) is given by the parametric function. x = a(t) cos(3nt) + b(t)cos 4πt y = a(t) sin(3πt) + b(t)sin (4) where a(t) and b(t) are functions of time. Both x and y are measured in metres. a) Show the squared distance from the origin, i.e. d² = x² + y²,can be written d² = (a(t))² + (b(t))² + 2a(t)b(t)cos ( b) If the functions a(t) and b(t) 5πt 5πt a(t) = 4+2cos 3 5πt b(t) = 1 -4cos (5) now show the squared distance from the origin, i.e. d² = x² + y², can be rewritten as d² = -16 cos³ -8 cos² 5nt '5πt' +16cos 5πt +17 c) Using (b) find algebraically all times, t≥0 (in exact form i.e. in terms of fractions) when the distance d is 3 mi.e. d = 3 or d² = 9. Hint. periodic solutions can be represented in the form t = a + nT where a is one solution, T is the period, and n is an integer n = 0,1 ....
Parametrize the intersection of the surfaces y² - z² = x - 6, y² + z² = 25 using trigonometric functions. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the parametrization of the y variable in the form a cos (t).) x(t) = y(t) = z(t) =
Please show every step of the solution by using the parametric formula version of the surface area. Thanks !
d) A set of parametric equations is given as x =- cott and y= cost, 0
The surface parametrized by r(u, v)=(5 cos u sin v, 5 sin u sin v, 5 cos v) is a
Please help me with this problem given for test practice! THANK YOU SO MUCH!!
Parametrize the intersection of the surfaces y- z = x - 5, y + z? = 4 using trigonometric functions. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the parametrization of the y variable in the form a cos (1).) x(t) = y(t) = z(t) =