Show by carrying out the integration that sin (mx / a) and cos (mx / a), where

Question:

Show by carrying out the integration that sin (mπx / a) and cos (mπx / a), where m is an integer, are orthogonal over the interval 0 ≤ x ≤ a. would you get the same result if you used the interval 0 ≤ x ≤ 3a/4? Explain your result.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Physical Chemistry

ISBN: 978-0321812001

3rd edition

Authors: Thomas Engel, Philip Reid

See More Books

Question Posted: Apr 30, 2018 04:24 AM

See More Questions

Show that and sin 20; sin 20, (4.98) sin?(0; + 0,) cos(0; 6,) sin 20; sin 20, T1 sin (0; + 0) (4.99)
Show by carrying out the appropriate integration that the total energy eigenfunctions for the harmonic oscillator 0 (x) ( /) 1/4 e -(1/2)ax2 and 2 (x) ( /4) 1/4 (2x - 1) e -(1/2)ax2 are orthogonal...
The motion of a charged particle in an electromagnetic field can be obtained from the Lorentz equation for the force on a particle in such a field, if the electric field vector is E and the magnetic...
In 2020, A corporation gave the following fringe benefits to its employees (Non-resident alien not engaged in trade/business): To managerial employees - P1,500,000 To rank and file employees -...
Assume that you expect to hold a $40,000 investment for one year. It is forecasted to have a yearend value of $42,000 with a 30% probability; a year end value of $48,000 with a 45% probability; and a...
The bar graph shows the population of the United States, in millions, for seven selected years. Here are two functions that model the data: Use the functions to solve Exercises 9798. a. Write a...
* explore implications for the nature of leading and managing change.
Arnold Industries has pretax accounting income of $33 million for the year ended December 31, 2011. The tax rate is 40%. The only difference between accounting income and taxable income relates to an...
Erin Shelton, Inc., wants to earn a target profit of $850,000 this year. The company's fixed costs are expected to be $1,100,000 and its variable costs are expected to be 60 percent of sales. Erin...
Allie has bought a new apple orchard. The orchard has a single file of trees, numbered from 1 to N. Each tree has a certail number of ripe apples. Allie has a rule she wants to follow. She wants to...
Use a Fourier series expansion to express the function f (y) = y 2 , b ¤ y ¤ b, in the form Obtain d 0 and the first five pairs of coefficients c n and d n . cos f0) -d0+ , sin |+ dc...
To plot Î¨(x, t) = Asin (kx Ït) as a function of one of the variables x and t, the other variable needs to be set at a fixed value, x 0 or t 0 . If Î¨(x 0 , 0) / Î¨...
See Table 2.5 showing financial statement data and share price data for Mydeco Corp. Suppose Mydeco had purchased additional equipment for $$12$ million at the end of 2010, and this equipment was...
Joint Ventures are a common Mode of Entry in international business. Appreciate if in-depth elaboration provided on its advantages and disadvantages. Also briefly mention the factors which make joint...
The field excursion is intended to give students an opportunity to carry out an applied geographical research project based on observation, data recording, and analysis. Using a field site of your...
An angry coworker is expressing their needs through a rush of emotion and snide comments while another coworker is trying to interpret them to provide some help and support. You are a manager and...
You may have a general understanding of the difference between ethics and legality , but could you explain the distinction? It is not always easy to know where to draw the line between the two. Some...
Someone can be a good leader but not be a very good manager and vice-versa. Leadership is creating a vision for others to follow, establishing corporate values and ethics, and transforming the way...
Use implicit differentiation to find d 2 y/dx 2 if 3x 2 2y 2 = 6.
For liquid water the isothermal compressibility is given by; where r and b are functions of temperature only. If 1 kg of water is compressed isothermally and reversibly from I to 500 bar at 60(C. how...
Given that the density of air at 0.987bar and 27C is 1.146 kg m 3 ,calculate the mole fraction and partial pressure of nitrogen and oxygen assuming that (i) Air consists only of these two gases, (ii)...
Balloons are still used to deploy sensors that monitor meteorological phenomena and the chemistry of the atmosphere. It is possible to investigate some of the technicalities of ballooning by using...
Derive an expression for v n 1/n from the MaxwellBoltzmann distribution of speeds. You will need standard integrals given in the Resource section.
Your company produces a health magazine. Its sales data for 1 - year subscriptions are as follows: Year of Operation Subscriptions Sold % Expired at Year End 2 0 2 0 $ 3 0 0 , 0 0 0 5 0 2 0 2 1 $ 6 4...
The adjusted trial balance for Tybalt Construction on December 3 1 of the current year follows. TYBALT CONSTRUCTION Adjusted Trial Balance December 3 1 Number Account Title Debit Credit 1 0 1 Cash $...
( US$ millions ) 1 2 / 3 1 / 2 0 1 4 1 2 / 3 1 / 2 0 1 3 1 2 / 3 1 / 2 0 1 2 1 2 / 3 1 / 2 0 1 1 Net income $ 1 4 , 4 3 1 $ 1 2 , 8 5 5 $ 1 0 , 7 7 3 $ 9 , 7 7 2 Depreciation 3 , 5 4 4 2 , 7 0 9 1 ,...

Show by carrying out the integration that sin (mx / a) and cos (mx / a), where

Question:

Step by Step Answer:

Except for the special case 3m4 n where n is an integer The len...View the full answer

Physical Chemistry

Students also viewed these Sciences questions