Purchase Solution

Real Analysis : Integrable Functions

Not what you're looking for?

Ask Custom Question

Let f:[0,1]-->R be a Riemann integrable function. Prove that
lim n-->∞ ∫ (from 0 to 1) x^n f(x)dx = 0.

I do not know where to begin on this problem. It seems like it should be easy though.

Purchase this Solution
Solution Summary

An integrable functions proof is provided in the solution.

Solution Preview

It is evident that x comes from [0, 1]. So lim n-->∞ (x^n)=0
Give that f is Riemann integrable function. Hence f must be bounded. Let the bounds of f are m and ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Riemann integrable

    This solution helps explore Reimann Integrable functions within the context of real analysis.

  • Real Analysis :Problem Prove a function is integrable over [a,b]

    11554 Real Analysis :Problem Prove a function is integrable over [a,b] Let f:[a,b] mapped to the Reals be a function that is integrable over [a,b], and let g:[a,b] mapped to the Reals be a function that agrees with f except at two points.

  • Step Functions and Riemann Integrals

    89862 Real analysis - Step Functions and Riemann Integrals If f is defined on [a,b] and and are, respectively, a nondecreasing and a nonincreasing sequence of step functions such that for all k and all and for almost all , show that f is Riemann

  • Real Analysis : Riemann Integrable Functions

    103513 Real Analysis : Riemann Integrable Functions Show that the function h, defined on I by h(x)=x for x rational and h(x)=0 for x irrational, is not Riemann integrable on I. Please see the attached file for the complete solution.

  • Real Analysis: Criteria for Integrability

    9874 Real Analysis: Criteria for Integrability Define f(x) = x^2 for all x in [0,1].

  • Real analysis - Lebesgue Integral

    Section 7 Notes: The Lebesgue Integral Definition 7.1 Let L be the set of real-valued functions f such that for some g and h in (see attached) f=g-h almost everywhere.

  • Real analysis: Lebesgue Integral

    89872 Real analysis: Lebesgue Integral Prove theorem 7.3 in notes attached. Section 7: The Lebesgue Integral Definition 7.1 Let L be the set of real-valued functions f such that for some g and h in f=g-h almost everywhere.

  • Real analysis

    Please see attachment This is a proof regarding limits of integrable functions.

  • Real analysis

    This is a proof regarding limits of integrable functions.

View More Related Solutions