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Lecture

7.3 Trigonometric Substitution Question #4 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
7.3 Integration Techniques Trigonometric Substitution Question #4 (Medium): Evaluating Complex Integral Using Trigonometric Substitution Strategy There are three forms of trigonometric substitution as follows: For √ , use . For√ , use . For √ , use . But if one of the three is not obvious from the beginning, then check out the expression usually within the square root (but not always!) and try to convert to perfect square. Then it should fall into one of the three categories, so then proceed as usual with trig substitution. Sample Question Evaluate the integral. ∫ ( ) Solution Typical square root is not there. Notice the denominator contains quadratic function. Completing the square: ( ) ( ) ( ) ( ) √ Then it follows the for√ , so can be used. Let √ , then √ and √ . Then:∫( ) ∫ (√ ) ∫ (√ ) √ ∫ √ √ . Based on (( ) √ ) ((√ ) √ )
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