# Integration: Cauchy-Schwarz Inequality

Not what you're looking for?

Suppose that the functions g:[a,b]-> R are continuous. Prove that:

The integral from a to b of gf <= (the square root of the integral from a to b of g^2) multiplied by (the square root from a to b of f^2)

##### Purchase this Solution

##### Solution Summary

The Cauchy-Schwarz inequality is used to prove an integral relation.

##### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

We want to show that:

≤

A good method of considering this problem is to narrow it down to an inner product problem. First we must show that theses integrals actually represent inner products:

An inner product should have the following properties:

1- <x, x> >= 0 and <x, x> = 0 if and only if x=0

2- <y, x> = <y, x>

3- <cx, y> = c<x, y>

4- <x+y, z> = <x, z> + <y, z>

I just show you the first feature in this ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### 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.

##### Probability Quiz

Some questions on probability