A nonintegrable function Consider the function defined on [0, 1] such that f(x) − 1 if x is a rational number and f(x) = 0 if x is irrational. This function has an infinite number of discontinuities, and the integral
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
- 8. Find the area between the x-axis and the graph of f (x) =1/x between a) 1 and 2 b) 1 and e9. Consider the denite integralCompute the left and right Riemann sums approximating this integralusing a uniform partition of n subintervals where a) n = 5 b) n = 10Present your answers as approximations, accurate up to three or more decimal places.arrow_forwardIn applications it is sometimes useful to use an approximation for factorials. The factorial of a positive integer n is defined to be the number n! = 1 · 2 · 3 · · ·(n − 1) · n, e.g., 4! = 1 · 2 · 3 · 4 = 24.Noticing that F(x) = x ln x − x is an antiderivative of f(x) = ln x, use the definition of the definite integral (Riemann sums) to show thatln(n!) ≈ n ln n − n. is a good approximation of ln(n!) for large values of n.arrow_forward
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage