How do you know when it's time for Trignometric Subsitution ?

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In summary, the best time to use trigonometric substitution is when it simplifies the integrand significantly, particularly when you see a 1 and an x^2. Other indicators include seeing something like \frac{1}{\sqrt{1+x^2}} or \frac{1}{\sqrt{1-x^2}}, or when the integrand resembles the derivative of an inverse trig function. It is always helpful to try solving without the substitution first, and only resort to it if necessary.
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jkh4
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How do you know when it's time for "Trignometric Subsitution"?

How do you know when it's time for "Trignometric Subsitution"?
 
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  • #2
You should be more specific about that question.
 
  • #3
it an integration technique. it should always "work". sometimes it just makes things easier.
 
  • #4
jkh4 said:
How do you know when it's time for "Trignometric Subsitution"?
Whenever a trigonometric substitution simplifies your integrand significantly.
 
  • #5
Usually when you see something like [tex]\frac{1}{\sqrt{1+x^2}}[/tex] or [tex]\frac{1}{\sqrt{1-x^2}}[/tex] or anything similar then you can think about using a trig sub. I usually think of trig sub when I see somethign that looks like the derivative of an inverse trig functions. (you should memorize those). But there are definitely many cases where a trig sub could be used...
 
  • #6
basically whenever you see a 1 and an x2, you can do some sort of trig or hyperbolic trig substitution to make things easier. Of course, if you're not sure, try solving it without the substitution, and only if you get stuck should you go for it (since if it's not useful, it can be a real pain in the ass trying to figure that out).
 

FAQ: How do you know when it's time for Trignometric Subsitution ?

How do you know when it's time for Trignometric Subsitution?

Trignometric substitution is used when an integral contains a combination of algebraic and trigonometric functions. This can be identified by looking for expressions such as sqrt(a^2-x^2) or sqrt(x^2-a^2) which can be rewritten using trigonometric identities.

What are the benefits of using Trignometric Subsitution?

Trignometric substitution can simplify integrals and make them easier to solve. It can also be used to solve integrals that cannot be solved using other methods.

How do you choose the appropriate trigonometric substitution?

The choice of trigonometric substitution depends on the form of the integral. Common substitutions include using sin^2(x) and cos^2(x) to rewrite expressions containing sqrt(a^2-x^2) or sqrt(x^2-a^2), and using tan(x) to rewrite expressions containing sqrt(a^2+x^2).

Can Trignometric Subsitution be used for all integrals?

No, trignometric substitution is only useful for certain types of integrals that contain a combination of algebraic and trigonometric functions. It cannot be used for integrals that do not have this form.

Are there any limitations to using Trignometric Subsitution?

One limitation of trignometric substitution is that it can only be used for integrals that contain a combination of algebraic and trigonometric functions. It may also not be the most efficient method for solving certain integrals, and other techniques such as integration by parts or partial fractions may be more suitable.

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