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 | + | *[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 | + | *[https://youtu.be/MdsAvt9y5ds Integrating using Inverse Trigonometric Functions] by patrickJMT |
+ | |||
+ | ==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
Contents
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
- Integration into Inverse trigonometric functions using Substitution by The Organic Chemistry Tutor
- Integrating using Inverse Trigonometric Functions by patrickJMT
Licensing
Content obtained and/or adapted from:
- Integrals Resulting in Inverse Trigonometric Functions, LibreTexts: Mathematics under a CC BY-SA-NC license