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Lecture

7.1 Integration by Parts Question #4 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
7.1 Integration Techniques Integration by Parts Question #4 (Medium): Solving Definite Integral Strategy Sometimes integration by parts can be applied right away. But sometimes given expression needs to be simplified first, and grouped in certain way so that one of the components can be expressed in a form of the chain rule. In that case, let the function in the form of the chain rule band the other function . Then plugging into the integral of integration by parts is as follows: ∫ ( )[ ( ( )) ( ) ] [ ( ) ( ( ))] ∫ ( ( )) ( ) , where ( ( )) ( ) , ( ( ) , and ( ), ( ) . Sample Question Evaluate the definite integral using integration by parts. ( ) ( ) ∫ Solution The integral contains two functions that cannot be simplified any further. However, it is after some kind ( ) of chain rule where ( ) comes from . Trying to relate the two, double angle can be ap
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