Difference between revisions of "Integrals Resulting in Inverse Trigonometric Functions"

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==Resources==
 
==Resources==
[https://youtu.be/AE-0gXXx_j0 Integration into Inverse trigonometric functions using Substitution] by The Organic Chemistry Tutor
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*[https://youtu.be/AE-0gXXx_j0 Integration into Inverse trigonometric functions using Substitution] by The Organic Chemistry Tutor
  
[https://youtu.be/MdsAvt9y5ds Integrating using Inverse Trigonometric Functions] by  patrickJMT
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*[https://youtu.be/MdsAvt9y5ds Integrating using Inverse Trigonometric Functions] by  patrickJMT
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==Licensing==
 +
Content obtained and/or adapted from:
 +
* [https://math.libretexts.org/Courses/Monroe_Community_College/MTH_211_Calculus_II/Chapter_5%3A_Integration/5.7%3A_Integrals_Resulting_in_Inverse_Trigonometric_Functions_and_Related_Integration_Techniques Integrals Resulting in Inverse Trigonometric Functions, LibreTexts: Mathematics] under a CC BY-SA-NC license

Revision as of 14:34, 28 October 2021


Example 1

Evaluate the integral

Solution

Substitute . Then and we have

Applying the formula with we obtain

Example 2

Evaluate .

Solution

This integral requires two different methods to evaluate it. We get to those methods by splitting up the integral:

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The first integral is handled straightforward; the second integral is handled by substitution, with . We handle each separately.

: Set , so . We have

Combining these together, we have

Resources

Licensing

Content obtained and/or adapted from: