Question: (5.2) Consider the integral 2 1 I = 2 ( x 2 + y2 ) dt, and the 1-parameter transformation x = x cosa +

(5.2) Consider the integral 2 1 I = 2 ( x

(5.2) Consider the integral 2 1 I = 2 ( x 2 + y2 ) dt, and the 1-parameter transformation x = x cosa + y sin a, y = y cosa - x sina, t = t. (a) Show that the given integral I is invariant under the given 1-parameter transformation. (6) (b) Use Noether's theorem and part (5.2(a)) to show that xy - xy is constant along an extremal of (6) the Lagrangian L( x, y ) =

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

8. [0/1 Points] PREVIOUS ANSWERS SCALCET9 15.4.032. ASK YOUR TEACHER PRACTICE ANOTHER (a) A lamp has two bulbs, each of a type with average lifetime 1,700 hours. Assuming that we can model the...

Evaluate the following integral using trigonometric substitution. 7 - - dx - 1 1+ x2 13 What substitution will be the most helpful for evaluating this integral? O A. x = sin 0 O B. x= sec0 C. x = tan...

Math 1242-006 Dr. Taylor Test I Review Name: ____________________ HW#1 Chapter 5.1 and 6.1 (Print Last Name First!) You must show all your work in the provided space to receive credit - even on the...

Shawn Simard Assignment Section 13.6 due 12/01/2016 at 11:59pm MST 1. (1 point) Match the parametric equations with the verbal descriptions of the surfaces by putting the letter of the verbal...

s 1. Find the center of mass of the following plane region with variable density. Describe the distribution of mass in the region: The upper half (y 0) of the y 2 2 disk bounded by the circle x + y...

Summer Semester 2016 MATH 22: Calculus II - Final You have 1 hr. 45 min. to complete this exam. Show all of your work, simplify your answers fully and box them. There are no notes, no calculators, no...

How to solve these three question? 1. (2 marks) Consider the integral 5 1= x20 (4-22 dx . For this kind of integral we usually use the substitution x = 2 sin 0 or x= 2cos0 x = 2sinh0 x = 2cosh0 ( x =...

there are 4 questions which all are answered I just want someone to double check them and give corrections (do please dont type it) thanks. div ( v ) = ( d /ax, a/ ay, 2 / 72). (4- 2 x42 - xe cos (y...

22 cos(2-x) sin(2-x)dx 51. dx COS X 24. cos 3x dx 26. cos cos 498 y sin y dy /3 53. tan x dx /4 55.secx dx -/4

Show that span (u, v) = span (u, u + v) for any vectors u and v.

Show e^(-2*x*y)*((sin(x^2-y^2)-i*cos(x^2-y^2)) as an analytic function of z

evaluate the given integral b y changing t o polar coordinates. 9 . e - x 2 - y 2 d A , where D i s the region bounded b y the semi - circle x = 4 - y 2 2 and the y - axis

Fashion Fabrics makes pants from a special material. The fabric is special because of the way it fits many body types. The pants sell for $142. A well-known retail establishment has asked Fashion...

The Walton Toy Company manufactures a line of dolls and a doll dress sewing kit. Demand for the dolls is increasing, and management requests assistance from you in determining an economical sales and...

Sanderson Manufacturing produces ornate, decorative wood frame doors and windows. Each item produced goes through 3 manufacturing processes: cutting, sanding, and finishing. Each door produced...

Edwin Edwards and Karen Davis owned EEE, Inc., which owned three convenience stores, all of which sold gasoline. Reid Ellis delivered to the three convenience stores $26,675.02 worth of gasoline for...

The following selected events occurred for a company during 2010: Jan. 11 A motor breaks on a machine and is replaced for $800. This replacement was expected when the machine was purchased. Jan. 25 A...

Among a group of 5 8 programmers, who know either Java or Python or both, 1 5 only know Java and 1 3 only know Python. What is the probability of randomly choosing a programmer who knows both...

Job costing for the movies. Movies and television shows are jobs. Some are successful, some are not. Studios must decide what to do with the cost of unsuccessful shows ("flops"). Some studios have...

Analyzing costs in a job company. On June 1. Wells Landscaping Company had two jobs in process with the following costs: In addition, overhead is applied to these jobs at the rate of 100 percent of...

Computing equivalent units and cost flows under process costing (Appendix 2.1). Omar Production Company has a process cost accounting system. Omar incurred material, direct labor, and manufacturing...