Concept explainers
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
Trending nowThis is a popular solution!
Chapter 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
- Evaluate 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_forwardBasic Intergration Rules Evaluate the following integrals. Check by differentiation. ∫ ( x 4 − 4 x ) d xarrow_forwardDepreciation 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_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_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