Possible webpage title: Solving Integrals Using the Substitution Method

In summary, the conversation discusses evaluating the integral of 1/(1-sin2u)×cosu using integration by substitution. The solution obtained is u + c = sin-1x + c, but it is suggested to try u=1-x^2 instead for an easier approach.
  • #1
roam
1,271
12
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,

 
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  • #2
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
Try u=1-x^2 instead... Might be a bit easier.
 

What is the Substitution Method?

The Substitution Method is a mathematical technique used to solve systems of equations with two variables. It involves isolating one of the variables in one equation and substituting its value into the other equation.

When is the Substitution Method used?

The Substitution Method is used when solving systems of equations where one of the equations can be easily solved for one of the variables. It is often used as an alternative to the Elimination Method.

How do I use the Substitution Method?

To use the Substitution Method, first solve one of the equations for one of the variables. Then, substitute the expression for that variable into the other equation. This will result in an equation with only one variable, which can then be solved for its value. Finally, substitute this value back into the original equation to find the value of the other variable.

What are the advantages of using the Substitution Method?

The Substitution Method can be useful when one of the equations already has a variable isolated, making it easier to find the value of that variable. It can also be used for systems of equations where the coefficients of one variable are the same in both equations, which makes the substitution simpler.

Are there any limitations to the Substitution Method?

The Substitution Method can only be used for systems of equations with two variables. It also requires one of the equations to be easily solvable for one of the variables. In some cases, the resulting equation after substitution may be more complicated to solve than the original system of equations.

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