Class Notes (807,036)
Mathematics (2,710)
MAT136H1 (776)
all (232)
Lecture

# 7.3 Trigonometric Substitution Question #1 (Easy)

1 Page
114 Views

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 √ √
More Less

Related notes for MAT136H1

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.