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Lecture

# 7.3 Trigonometric Substitution Question #1 (Easy)

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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 #1 (Medium): Evaluating the Integral Using Sine Substitution Strategy When the function is in the form of √ , then use sine substitution where and . Based on the identity , under the square root simplifies to . Combined with substitution, apply half angle identity ( )which makes taking the anti-derivative much easier. Then change the anti-derivative into based on the double-angle formula so that plugging in the original variable is much easier. Draw the right angle triangle with angle and the opposite and hypotenuse sides labeled based on the substitution . Find the adjacent side based on the Pythagorean Theorem, and this expression should equal to the original expression in the integral √ . Sample Question Evaluate the integral. ∫√ Solution Since the integral is in the form of √ , sine substitution is appropriate. Given integral can be written as √ √
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