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Lecture

# 7.3 Trigonometric Substitution Question #2 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
7.3 Integration Techniques Trigonometric Substitution Question #2 (Medium): Evaluating the Integral Using Tangent Substitution Strategy For the expressio√ let . Then . Substitute into the expression √ ( ) √ √ √ based on the identity . Then combined with other expressions, simplify the integral and then evaluate using various tricks learned so far. Sample Question Evaluate the integral. ∫ √ Solution First, denominator needs to be expressed in terms of squares. Perfecting the squares: √ √ ( ) √ ( ) , then tangent substitution can be used, since it follows after the form √ . Then, ; , and . So substitute to the integral∫ ∫ ∫ ∫ √ √( ) √ ( ) √ ∫ . Based on
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