Question: For each a, b E R, consider B(a, b) = f t-1 (1 t)b-1 dt. (a) For which values of a and b the

For each a, b E R, consider B(a, b) = f t-1 (1 t)b-1 dt. (a) For which values of a and b the integral B(a, b) is an improper integral? (b) Show that the integral converges when a > 0 and b > 0. (c) Show that the integral diverges if either a 0 or b 0. (d) Using t= sin(0)2 show that for a, b> 0 we have /2 255/2 B(a, b) = 2 sin (0)2a-1 cos(0)26-1 do.

Step by Step Solution

★★★★★

3.33 Rating (147 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The integral Bab is an improper integral if either a 0 or b 0 This ... View full answer

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 Accounting Questions!

Sketch the region of integration and evaluate the integral Rxy dV where R is the solid tetrahedron with vertices (2,0,0), (3,3,0), (3,3,3) and (0,3,0).

Show that the polar equation r = a sin + b cos , where ab 0, represents a circle, and find its center and radius.

If J = r sin cos ar cos 2 sin a + tan /2 In r a at T(2, /2, 3/2), determine the vector component of J that is (a) Parallel to az (b) Normal to surface = 3/2 (c) Tangential to the spherical surface r...

A paper by R.N. Rodriguez (Health Care Applications of Statistical Process Control: Examples Using the SAS® System, SAS Users Group International: Proceedings of the 21st Annual Conference, 1996)...

Suppose you want to take a sample of students in a university but your sampling frame is a list of all classes offered by the university. A student may be in more than one class, so a probability...

Consider the investment projects given in Table P7.49. Assume that MARR = 15%. (a) Compute the IRR for each project. (b) On the basis of the IRR criterion, if the three projects are mutually...

In Example 4.1, estimate a variance transformation model with $\log \left(\sigma_{i}^{2} ight)=\xi_{0}+\xi_{1} \mu_{i}$, and compare its fit with a constant variance normal linear regression using...

Consider the algorithm in figure to compute ?+. Show that this algorithm is more efficient than the one presented in Figure (Section 7.3.3) and that it computes ?+ correctly. result := 0; /* fdcount...

Carl Beers Enterprises manufactures and sells specialized electronic components to customers across the country. The tables in Figure illustrate some of the records in its accounting databases. Thus,...

Souder, Oles, and Franek is an international consulting firm headquartered in Chicago, Illinois. The Entity-Relationship diagram in Figure shows a simplified version of the companys process for...

Question 15) A contribution to a traditional IRA may be tax deductible. Assuming your taxpayer meets the age and compensation requirements, what factor(s) determine whether their contribution is...

answer management interview questions 1-Describe your skills, knowledge, and experience in managing office policies and procedures, such as developing and implementing project proposals, budgets, or...

Once a strategy for performance improvement has been determined, how can organizations gain the long-term commitment and investment of time required by all levels of the organization to implement the...

What makes the store manager of a retail company a classic example of an operations manager. Hint: please refer to large retail companies

Consider the following workplace research example: Within one company division, employees were asked to create self-managed work groups in order to accomplish an important company objective. Leaders...

Define and describe the types of manufacturing, services, and extraction industries. Give examples. 2. What are the various categories of services? Give examples for each category? 3. How do services...

Suppose a firm projects a $4 million perpetuity from an investment of $18 million in Spain. If the required return on this investment is 17%, how large does the probability of expropriation in year 4...

(a) How far away can a human eye distinguish two ear headlights 2.0 m apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 mm and a wavelength of 550 nm. (b) What is the...

Prove that the distance between parallel planes with equations n x = d1 and n x = d2 is given by |d1 - d2| / ||n||.

In Exercises 1-3, describe the span of the given vectors (a) geometrically and (b) algebraically. 1. 2. 3. -4, 2. 2.

(a) A = (1, - 1), B = (4, 2) (b) A = (0, - 2), B = (2, - 1) (c) A = (2, 3/2), B = (1/2, 3) (d) A = (1/3, 1/3), B = (1/6, 1/2) AB

Exercise 4 gave data on mass loading and mass removal. Values of relevant summary quantities are a. Obtain the equation of the least squares line. b. Predict the value of BOD mass removal for a...

Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (F) in the chamber in which the reaction takes place according to the simple linear regression model...

The accompanying data was read from a graph that appeared in the article Reactions on Painted Steel Under the Influence of Sodium Chloride, and Combinations Thereof (Ind. Engr. Chem. Prod. Res. Dev.,...