How to solve ∫ytan^-1(y) dy using integration by parts?

Thread starter anna062003
Start date Mar 2, 2012
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Trigonometric

In summary, trigonometric substitution is a technique used in calculus to simplify integrals involving expressions with square roots, using trigonometric identities. It is often used when the integrand involves an expression of the form x^2 + a^2, x^2 - a^2, or a^2 - x^2, where a is a constant. The three main trigonometric substitutions are for x^2 + a^2, x^2 - a^2, and a^2 - x^2, which involve substituting x with a tan θ, a sec θ, or a sin θ, respectively. Using trigonometric substitution can help to simplify difficult integrals and uncover hidden symmet

Mar 2, 2012

anna062003

Evalutate ∫ytan^-1(y) dy

i don't know how to start, can somebody tell me how?

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Mar 2, 2012

Dick

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anna062003 said:

Evalutate ∫ytan^-1(y) dy

i don't know how to start, can somebody tell me how?

It's not a trig substitution problem, it's an integration by parts problem. Try u=arctan(y) and dv=ydy.

FAQ: How to solve ∫ytan^-1(y) dy using integration by parts?

What is trigonometric substitution?

Trigonometric substitution is a technique used in calculus to simplify integrals involving expressions with square roots, using trigonometric identities.

When is trigonometric substitution used?

Trigonometric substitution is often used when the integrand involves an expression of the form x² + a², x² - a², or a² - x², where a is a constant.

What are the three main trigonometric substitutions?

The three main trigonometric substitutions are the substitution for x² + a², the substitution for x² - a², and the substitution for a² - x². These involve substituting x with a tan θ, a sec θ, or a sin θ, respectively.

What are the benefits of using trigonometric substitution?

Trigonometric substitution can be used to simplify integrals that would otherwise be difficult to solve, especially those involving square roots and rational functions. It can also help to uncover hidden symmetries in the integrand.

What are some common mistakes when using trigonometric substitution?

Some common mistakes when using trigonometric substitution include forgetting to change the limits of integration, substituting incorrectly, and not properly simplifying the resulting integral. It is important to carefully follow the steps and check your work to avoid these mistakes.