Evaluate integral using substitution

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Homework Help Overview

The problem involves evaluating the integral of the function cos-1x divided by the square root of (1 - x2) with respect to x, using substitution techniques. The subject area pertains to integral calculus and the application of substitution methods in integration.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses frustration with the integration process and seeks guidance on how to set up the problem. Some participants suggest considering the derivative of cos-1x as a potential approach to substitution. Others confirm the correctness of the derivative and discuss the implications for substitution.

Discussion Status

The discussion is ongoing, with participants exploring the setup for substitution and confirming the relationships between the integrand and its derivative. There is an exchange of hints and confirmations regarding the substitution process, but no explicit consensus on the final outcome has been reached.

Contextual Notes

The original poster is new to integration and is looking for foundational support to understand the setup of the problem, indicating a potential lack of familiarity with integration techniques.

Col Musstard
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Homework Statement


evaluate using substitution
Integral [cos^-1 x]/sqrt[1-x^2] dx

Homework Equations





The Attempt at a Solution


I am just starting with integration and I am getting frustrated with this problem. If someone could show me how to setup and start this problem so I could attempt to continue by reading instructions from my textbook it would be greatly appreciated
 
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Hint: What's the derivative of [itex]cos^{-1} x[/itex]?
 
that is -1/sqrt[1-x^2] isn't it
 
Yup. Note that it's the other part of the integrand, so that means you should use a substitution.
 
so u=cos^-1x. therefore du=-1/sqrt[1-x^2] dx
is this correct so far?

I got -[[cos^-1x]^2]/2 +c hope its right, thanks for the help
 
Last edited:
Yes, that's the correct answer. You can always differentiate what you got and see if you get back the integrand.
 

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