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

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In summary, the conversation discusses the process of solving the integral 2x((1-x^2)^(1/2)) and the challenges the person has faced. They have tried integration by parts and substitution, but have not been successful. The conversation also mentions the need to find the integral when x=1 and the issue of getting 0 in the numerator. The suggested approach is to use the chain rule and a suggestion to try u=1-x^2. The conversation also mentions that getting 0 in the numerator is not a major issue, but the problem arises when the denominator equals 0.
  • #1
Wi_N
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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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  • #2
You can use the chain rule for this integral. It is straightforward.
 
  • #3
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##?
 
  • #4
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:


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What is the equation for "Integral 2x((1-x^2)^(1/2))"?

The equation is ∫2x√(1-x^2)dx.

What is the purpose of this integral?

This integral is used to find the area under the curve of the function 2x((1-x^2)^(1/2)).

What are the limits of integration for this integral?

The limits of integration for this integral are determined by the range of x values for which the function is defined. In this case, the limits are typically -1 to 1.

Is this an indefinite or definite integral?

This is a definite integral, as it has specific limits of integration.

What methods can be used to solve this integral?

There are various methods that can be used to solve this integral, including substitution, integration by parts, and trigonometric substitution.

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