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Lecture

7.1 Integration by Parts Question #5 (Hard)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
7.1 Integration Techniques Integration by Parts Question #5 (Hard): Reduction Formula Strategy Reduction formula means a function that is raised to power of n can be recursively written in term of the function with lower power, and repeating the process, the integral can be eventually solved. To prove reduction formula, split the power into and , or even and depending on the function and its derivative (such as tangent, cotangent, cosecant, secant). Then apply integration by parts, simplify, and in the process there is a term which can be moved to the other side to be combined with the original integral. From there on through further simplifying process, the reduction formula is proven. Sample Question Prove the reduction formula using integration by parts. ∫ ( ) ∫ Solution Based on integration by part
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