Using the Trapezoidal Rule and Simpson's Rule In Exercises 1–10, use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Calculus
- Basic Intergration Rules Evaluate the following integrals. Check by differentiation. ∫ ( 6 x^3 − 4 x + 1 ) d xarrow_forwarda. Approximate the value of the integral by using rectangles. For your approximation use right endpoints and let n = 4 b. Evaluate the integral by interpreting it in terms of areas. Draw a picture c. Evaluate the integral using the Fundamental Theorem of Calculus Part 2 FTC2)arrow_forwardEvaluate the integral. Check your answer by differentiating. (Use C for the constant of integration.)arrow_forward
- Estimating Errors. Use error formulas to estimate the erros in approximating the integral, with n=4, using (a) the Trapezoidal Rule and (b) Simpson's Rule.arrow_forwardBasic Intergration Rules Evaluate the following integrals. Check by differentiation. ∫ ( x 4 − 4 x ) d xarrow_forwardEvaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.) 0.9 (csc 2? − cot 2?)2 d? 0.4 This is an integralarrow_forward
- Depreciation A company purchases a new machine for which the rate of depreciation can be modeled by dV/dt=10,000(t-6), 0 < = t < = 5 where V is the value of the machine after t years. Set up and evaluate the definite integral that yields the total loss of value of the machine over the first 3 years.arrow_forwardTable look-up integrals Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning