Show that S 2 also gives the exact value for b a x 3 dx and conclude, as in Exercise 63, that S N is exact for all cubic polynomials Show by counterexample that S 2 is not exact for integrals of x 4 Data From Exercise 63 For N even, divide a, b into N subintervals of width x b a N Set x j a j x, y ...

Data From Exercise 62 get Let fx x Then Ax b a2 and the endpoints are ...

Show that S 2 also gives the exact value for b a x 3 dx and

Question:

Show that S₂also gives the exact value for ∫^b_ax³ dx and conclude, as in Exercise 63, that S_Nis exact for all cubic polynomials. Show by counterexample that S₂ is not exact for integrals of x⁴.

Data From Exercise 63

For N even, divide [a, b] into N subintervals of width Δx = b − a/N. Set x_j= a + j Δx, y_j= ƒ(xj), and

s2= b-a 3N (V2j + 4y2j+1 + y2j+2)

(a) Show that Sy is the sum of the approximations on the intervals [X2, X2j+2]that is, Sy = S + S2 + ... +

Data From Exercise 62

that Show that if f(x) = px + qx +r is a quadratic polynomial, then S = = 6 f(x where yo = = f(a), y = f a +

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

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 15, 2024 07:00 AM

See More Questions

Show that if f(x) is a polynomial of degree less than n then f(x) must equal the interpolating polynomial P(x) in (7), and hence the sum in (7) gives the exact value for ba f(x)w(x)dx.
Show that the parabolic Rule gives the exact value of Provided that k is odd. .k x* dx
Show that from d' Alemberts solution (13) in Sec, 12.4 with c = 1 it follows that (6) in the present section gives the exact value uij+1 = u (ih, (j + 1) h).
Consider two farmers, A and B, produce farm products and sell in the same market. Assume that the supply of the two farmers products are the same but the demand for Farmer Bs product is relatively...
There are two isomeric conjugate acids that produce the following base. Show the structure of each and explain how they produce the same base upon loss of a proton. :0: CH3-C=CH
Prime Essentials Limited is a small private corporation. The owner plans to approach the bank for an additional loan or a line of credit to facilitate The bookkeeper has provided some notes on the...
Have you been involved in more than one breakup with a friend lately? True/False LO.1
On July 1, 2013, $6 million face amount of 7%, 10-year bonds were issued. The bonds pay interest on an annual basis on June 30 each year. The market interest rates were slightly higher than 7% when...
The ------------ market provides the means for transferring ownership of corporate securities. Select one: a. dealer b. auction c. primary d. secondary The time it takes to acquire and sell inventory...
According to Plancks Radiation Law, the amount of electromagnetic energy with frequency between and + that is radiated by a so-called black body at temperature T is proportional to F() , where...
(a) Divide the power series in Exercise 41 by 3x 2 to obtain a power series for h(x) = 1/(1 x 3 ) 2 and use the Ratio Test to show that the radius of convergence is 1. Data From Exercise 41...
The pin is used to connect the three links together. Due to wear, the load is distributed over the top and bottom of the pin as shown on the free-body diagram. If the diameter of the pin is 0.40 in.,...
6.10 Long Div. and Comp Square Calculus - No Calculator Find the indefinite integral. 1. S 4x-34x+56x-21 4x-2 dx Mastery Check #2 1 dx 2. Sx-4x+5x x-4x+5 S S Name: Sienna Nono Date: 3-1-24 Period:...
How well are oncology firms leveraging digital technology to gain and sustain competitive advantage?
Axel and Brooklyn have agreed to buy a new vehicle. Brooklyn mentions that she is looking forward to getting a new SUV, so they have room for their dogs and kids. Axel mentions he thought they were...
Discuss how technology and human resources are needed to operate this facility in this behind the scenes look at this retailing giant. Support your opinion with research and/or key concepts covered...
4.2 At a given instant, a spacecraft is 500 km above the earth, with a right ascension of 300 and a declination of -20 relative to the geocentric equatorial frame. Its velocity is 10 km/s directly...
Keesha earned x dollars per month in 2006, where x < $5,600. a. Did she earn more or less than the maximum taxable income for 2006? b. Express her Social Security tax for the year algebraically. c....
Juarez worked for Westarz Homes at construction sites for five years. Bever was a superintendent at construction sites, supervising subcontractors and moving trash from sites to landfills. He...
Show that an equation of the form Cy 2 + Dx = 0, C 0, D 0 is the equation of a parabola with vertex at and axis of symmetry the x-axis. Find its focus and directrix.
Show that the graph of an equation of the form Ax 2 + Dx + Ey + F = 0, A 0, (a) Is parabola if E 0. (b) Is a vertical line if E = 0 and D 2 - 4AF = 0. (c) Is two vertical lines if E = 0 and D 2 -...
Show that the graph of an equation of the form Cy 2 + Dx + Ey + F = 0, C 0, (a) Is parabola if D 0. (b) Is a vertical line if D = 0 and E 2 - 4CF = 0. (c) Is two vertical lines if D = 0 and E 2 -...
ABC Company engaged in the following transaction in October 2 0 1 7 Oct 7 Sold Merchandise on credit to L Barrett $ 6 0 0 0 8 Purchased merchandise on credit from Bennett Company $ 1 2 , 0 0 0 . 9...
Lime Corporation, with E & P of $500,000, distributes land (worth $300,000, adjusted basis of $350,000) to Harry, its sole shareholder. The land is subject to a liability of $120,000, which Harry...
A comic store began operations in 2018 and, although it is incorporated as a limited liability company, it decided to be taxed as a corporation. In its first year, the comic store broke even. In...

Show that S 2 also gives the exact value for b a x 3 dx and

Question:

s2= b-a 3N (V2j + 4y2j+1 + y2j+2)

Step by Step Answer:

Data From Exercise 62 get Let fx x Then Ax b a2 and the endpoints are ...View the full answer

Calculus

Students also viewed these Mathematics questions