Use the method of Example 4a or Equation (1) to evaluate the definite integral. Example 4a Compute
Question:
Use the method of Example 4a or Equation (1) to evaluate the definite integral.
Example 4a
Compute ∫0bx dx and find the area A under y = x over the interval [0, b], b > 0.
Transcribed Image Text:
To compute the definite integral as the limit of Riemann sums, we calculate lim-0 =1f(c) Ax for partitions whose norms go to zero. Theorem 1 tells us that it does not matter how we choose the partitions or the points c as long as the norms ap- proach zero. All choices give the exact same limit. So we consider the partition P that subdivides the interval [0, b] into n subintervals of equal width Ax = (b −0)/n = b/n, and we choose c to be the right endpoint in each subinterval. The partition is = P = 0. b 2b 3b n' n' n' .. nb 'n n kb and Ck = So n k=1 f(c) Ax kb b n n = = = = n = k=1 n 6² n² 6² 2 kb² n² n k n(n + 1) 2 1 + f(c) = Ck Constant Multiple Rule Sum of First n Integers
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 33% (3 reviews)
Step 1 Area u...View the full answer
Answered By
CHOWLA VINAY
I am an assistant professor and PhD student. I have published several articles and books. I am passionate about writing and research. Are you looking for an honest, reliable and happy teacher? Teaching and learning is second nature to me because my parents are teachers.
I did a lot of research and learned a lot of interesting and difficult things. All these experiences influenced my decision to pursue a teaching career in various capacities. As a teacher, I look forward to understanding your needs and helping you achieve your educational goals. I am flexible and easy to communicate with. I can study in a short time because I like to work only with small and outstanding students.
Interests: Business, Economics, Project Management, Sociology, Technology, Business, English, English, Media, Philosophy, Political Science, Statistics, Data Science, Excel, Psychology, Art, History, Art, Student Studies, Art, ethics, religion I am also very good at math and programming. If you have a project that you think I can do.
0.00
0 Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
Use the method of Example 4a or Equation (1) to evaluate the definite integral. Example 4a Compute 0 b x dx and find the area A under y = x over the interval [0, b], b > 0. To compute the definite...
-
Use the method of Example 4a or Equation (1) to evaluate the definite integral. Example 4a Compute 0 b x dx and find the area A under y = x over the interval [0, b], b > 0. To compute the definite...
-
Use the method of Example 4a or Equation (1) to evaluate the definite integral. Example 4a Compute 0 b x dx and find the area A under y = x over the interval [0, b], b > 0. To compute the definite...
-
Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables. OF -; F(u, v) = eu+v, u = x, v = xy
-
Ivan Abuzi is a house painter. He incurred the following costs during August 2009, when he painted four houses. In the ï¬rst week of August, Abuzi placed a $60 classiï¬ed ad for his...
-
Movie actors who win an Oscar usually can command a greater fee for their next motion picture. Does winning an Academy of Motion Picture Arts and Sciences award (aka, an Oscar) lead to long-term...
-
Have you ever bought a new (or used) car? What were the negotiations like? Did you enjoy the negotiations? Why or why not?
-
Perfect Pizza had the following account balances at December 31, 2010: Cash................ $ 33,000 Accounts receivable......... 15,000 Ingredients and supplies inventory. 10,000 Prepaid...
-
Draw the diagram in one color for the first move and then another color for the second move. 1. Move 1: Translate 5 units right and 1 unit up. Move 2: Rotate 90 clockwise around the origin. List the...
-
1) Create a dimensional model containing an aggregated fact table, where a fact table shows a summary of daily revenue amount for each officer. Use ERDPlus to create your model. 2) Populate the...
-
Express the solutions of the initial value problem in terms of integral. dy dx = sec x, y(2) = 3
-
If you do not know what substitution to make, try reducing the integral step by step, using a trial substitution to simplify the integral a bit and then another to simplify it some more. You will see...
-
Your supervisor has asked you to research a potential tax deduction for a client, Nancy Fradette. Nancy is a seat-filler at a number of the award shows that are filmed in the greater Los Angeles...
-
Strategize the best location for new hubs for the service arm and the best location and set up strategies for the manufacturing arm. In your calculations, consider methodologies such as: Weighted...
-
Using the Negotiation - Porto case, answer the buyer's questions in one paragraph and answer the seller's questions in another paragraph. Explain your answers in detail and provide external sources...
-
Compare and contrast between make-to-stock and make-to-order systems. In your comparison, why does each system require different types of contracts? What are the advantages and disadvantages of each...
-
Emissions reduction by battery power or alternative fuel cell cars is an area where research and development by existing players in the automobile industry could have substantial payoff and social...
-
For this problem, how do we get the values used for fixed asset turnover ratio? I understand that it is total revenue/net fixed asset. For total revenue we are given $3,269,404 but I am not sure what...
-
What are institutional investors? How are individual investors likely to be affected by institutional investors?
-
Consider the sections of two circuits illustrated above. Select True or False for all statements.After connecting a and b to a battery, the voltage across R1 always equals the voltage across R2.Rcd...
-
True False. The equation y 2 = 9 + 4x 2 is symmetric with respect to the x-axis the y-axis and the origin.
-
To graph y = (x 5) 3 4, shift the graph of y = x 3 to the (left/right) ____ units(s) and then (up/down) ____ unit(s).
-
Find the vertical asymptotes, if any and the horizontal or oblique asymptotes, if any of x - 9 x - 4
-
Consider Company X and Company Y; each firm wants to borrow 100 million for 3 years. Company X wants to finance an interest-rate-sensitive asset and therefore wants to borrow at a floating rate....
-
On December 3 1 , 2 0 2 3 , Corotel Company s year - end, the unadjusted trial balance included the following items: Account Debit Credit Accounts receivable $ 2 , 1 0 0 , 0 0 0 Allowance for...
-
Denton Company manufactures and sells a single product. Cost data for the product are given: Variable costs per unit: Direct materials $ 9 Direct labor 1 0 Variable manufacturing overhead 4...
Study smarter with the SolutionInn App