Integrate x^2/Sqrt[1 - x^2] - Solve 0=0

In summary, the conversation discusses different methods for finding the integral of (x^2)/ Sqrt(1-(x^2)), including using substitution and integration by parts. The conversation also touches on the importance of properly defining the variables used in integration by parts.
  • #1
huan.conchito
44
0
[tex]\!\(∫x^2/Sqrt[1 - x^2] \[DifferentialD]x\)[/tex]

I need to find the integral of
(x^2)/ Sqrt(1-(x^2))
if the above doesn't work properly
integration by parts results in 0=0 how do i do this?
 
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  • #2
You mean

[tex] \int \frac{x^{2}}{\sqrt{1-x^{2}}} \ dx [/tex]

How about the substitution [itex] x=\sin u [/tex] and then a nice trigonometrical identity involving a double angle...?

Daniel.
 
  • #3
It can be done by parts,too.

Daniel.
 
  • #4
ok, i got it using x= sinU
can you give me a hint how to do it using integration by parts?
 
  • #5
Integration by parts uses

[tex]\int u \ dv = uv - \int v \ du[/tex]

choose [itex] u = x[/itex] and

[tex] v = \frac{x}{\sqrt{1-x^2}}[/tex]

Edit: That should be [itex]dv = (x / \sqrt{1-x^2}) \ dx[/itex]!
 
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  • #6
Not really,Data.U needn't specify "u" & "v",but the factors in the LHS,"u" & "dv"...

So

[tex] u=x \ \mbox{and} \ dv=\frac{x}{\sqrt{1-x^{2}}} \ dx [/tex]

Daniel.

P.S.Data,u see the difference,right...?:rolleyes:
 
  • #7
indeed, silly me :-p~
 
Last edited:

FAQ: Integrate x^2/Sqrt[1 - x^2] - Solve 0=0

What is the formula for integrating x^2/Sqrt[1 - x^2]?

The formula for integrating x^2/Sqrt[1 - x^2] is ∫ x^2 / Sqrt[1 - x^2] dx = - 1/2 (1 - x^2)^(-1/2) + C.

How do you solve 0=0?

The equation 0=0 is an identity, meaning it is always true. Therefore, there is no need to solve it as it is already satisfied.

What is the domain of x^2/Sqrt[1 - x^2]?

The domain of x^2/Sqrt[1 - x^2] is all real numbers except for x = ±1, as the denominator becomes 0 at these values.

What is the graph of x^2/Sqrt[1 - x^2]?

The graph of x^2/Sqrt[1 - x^2] is a semicircle with a radius of 1, centered at the origin, and with the area under the curve bounded by the x-axis and the curve itself.

Are there any special techniques for integrating x^2/Sqrt[1 - x^2]?

Yes, there is a special trigonometric substitution that can be used to integrate x^2/Sqrt[1 - x^2]. This involves letting x = sinθ or cosθ and using trigonometric identities to simplify the integral.

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