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The Substitution Method

  • Thread starter roam
  • Start date
  • #1
1,266
11
Evaluate the following integral using integration by substitution: http://img254.imageshack.us/img254/750/44900023cm4.png [Broken][/URL]




Here is my attempt:
Let x = sinu, then dx/du = cosu
Substituting gives, ∫1/(1-sin2u)×cosu du
= ∫1/(1-sin2u)×cosu du
= ∫cosu/√cos2u du
= ∫cosu/cosu du
= ∫1 du = u + c = sin-1x + c

Am I right? Did I get the right solution?

Regards,

 
Last edited by a moderator:

Answers and Replies

  • #2
1,752
1
You don't need Trig sub. for this.

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

But we'll go with it!

[tex]x=\sin u[/tex]
[tex]dx=\cos udu[/tex]

[tex]\int\frac{\sin u \cos u du}{\sqrt{1-\sin^2 u}}[/tex]
 
  • #3
1,341
3
Try u=1-x^2 instead... Might be a bit easier.
 

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