Contour and fresnel integrals

Assignment Help Mathematics

Reference no: EM13128740

We want to calculate the integral of the function x*sin(x^4), from 0 to infinity.

We may think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I: 0 to R, II: theta = 0 to pi/4 and then finally to region III: R to 0 along e^i*pi/4. Now, this leads to the problem of integrating the function x*e^(i*x)^4.

A much simpler approach is suggested.

Reference no: EM13128740

Questions Cloud

Literature is the question minus the answer : Roland Barthes has said, "Literature is the question minus the answer." When you consider contemporary society what questions do you think are guiding authors and future authors?

Maximal interval of existence of initial value problem : Please solve the following initial value problem: We solve the initial value problem using separation of variables. We use partial fractions to solve for the integral of 1/(x^2-4).

Thomas company return on equity : The average stockholders' equity was $680,000. What is Thomas Company's return on equity (ROE)?

Example of government intervention : Governments have several means available to guide and influence competition in the marketplace. These means include government ownership of firms and industrial policy.

Contour and fresnel integrals : We may think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I: 0 to R, II:

Activity on a statement of cash flows : Which of the following should be classified as an investing activity on a statement of cash flows?

Define description of lipids : Description of Lipids 1) What are the ingredients of a cephalin? 2) Which fatty acid is always unsaturated in a cephalin? Why?

Calculate z-score and base response upon z-score : Would it be unlikely for them to find fewer than 65 children with the gene? Calculate the z-score and base your response upon the z-score.

How many sets with reservations for coach seats are possible : How many different sets of exactly 20 of the 23 people with reservations for coach seats are possible? (do you use permutations or combinations?)

User Account

All Pages