How to Solve the Integral 2x((1-x^2)^(1/2)) and Evaluate at x=1

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Homework Help Overview

The discussion revolves around evaluating the integral of the function 2x√(1-x²) and specifically determining its value at x=1. Participants are exploring various integration techniques and addressing challenges encountered during the process.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss attempts at integration by parts and substitution, expressing difficulty in progressing with the integral. Questions arise regarding the implications of the numerator being zero when evaluating at x=1, and suggestions are made to consider a substitution involving u=1-x².

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the setup of the integral. Some guidance is offered regarding the chain rule and the nature of the numerator being zero, but no consensus or resolution has been reached yet.

Contextual Notes

There is a noted concern about the behavior of the integral at the point x=1, particularly regarding the implications of a zero numerator. Participants are navigating the complexities of the integral without a clear resolution to the challenges presented.

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Homework Statement


Integral 2x((1-x^2)^(1/2))

Homework Equations

The Attempt at a Solution


ive tried integration by parts, i tried substitution and i can't get it to work. i also need to figure the integral when x=1 and i keep getting 0 in the numerator. What is the best point of attack?
 
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You can use the chain rule for this integral. It is straightforward.
 
Wi_N said:

Homework Statement


Integral 2x((1-x^2)^(1/2))

Homework Equations

The Attempt at a Solution


ive tried integration by parts, i tried substitution and i can't get it to work. i also need to figure the integral when x=1 and i keep getting 0 in the numerator. What is the best point of attack?
What happens when you try ##u=1-x^2##?
 
Wi_N said:

Homework Statement


Integral 2x((1-x^2)^(1/2))

Homework Equations

The Attempt at a Solution


ive tried integration by parts, i tried substitution and i can't get it to work. i also need to figure the integral when x=1 and i keep getting 0 in the numerator. What is the best point of attack?
From the way you've written the integrand, you don't have a denominator, so getting the numerator = 0 isn't that big a deal.

It's when the denominator = 0 that things blow up. :wink: :frown:


tsar-bomba1.jpg


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