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Lecture

# 7.3 Trigonometric Substitution Question #3 (Medium)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
7.3 Integration Techniques Trigonometric Substitution Question #3 (Medium): Evaluating the Integral Using Secant Substitution Strategy If it contains the expression √ then let and using the identity , simplify the expression. Then after the integral is solved, work with a right angle triangle and replace by substituting back in the original variable . Sample Question Evaluate the integral. ∫ √ Solution Since the denominator is in the form of √ , secant substitution is used. Let , then ( ) . Then:∫ ∫ . Simplifying: √ √ ( ) ∫ ∫ √ . Based on the identity : √ ∫ ∫ ∫ √ Use integration by parts to solve. Let and , and , then . Thus: [ ] [
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