Integrate arcsinw: Explaining the Result

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The discussion focuses on the integration of the arcsin function, specifically the expression "= warcsinw - integral of w/sqrt(1-w^2) = ...". Participants clarify that the result of the integration leads to the expression "sqrt(1-w^2) + C". The method used for this integration involves ordinary substitution, where u is defined as 1 - w² and du equals -2wdw. This substitution simplifies the integral and provides the necessary steps to arrive at the final result.

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  • Understanding of integral calculus
  • Familiarity with the arcsin function
  • Knowledge of substitution methods in integration
  • Basic algebraic manipulation skills
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  • Study the method of substitution in integral calculus
  • Explore the properties and applications of the arcsin function
  • Practice solving integrals involving square roots and trigonometric functions
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Students and educators in mathematics, particularly those focusing on calculus, as well as anyone seeking to deepen their understanding of integration techniques and the arcsin function.

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can someone explain what happened after the part where it says "= warcsinw - integral of w/sqrt(1-w^2) = ... " ? i don't see how they got sqrt(1-w^2) + C
 

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3ephemeralwnd said:
can someone explain what happened after the part where it says "= warcsinw - integral of w/sqrt(1-w^2) = ... " ? i don't see how they got sqrt(1-w^2) + C
Ordinary substitution, with u = 1 - w2, and du = -2wdw.
 
thank you!
 

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