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Lecture

7.1 Integration by Parts Question #2 (Easy)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
7.1 Integration Techniques Integration by Parts Question #2 (Easy): Solving Definite Integral Strategy When two entirely different functions that cannot be further simplified are given in the integral, integration by parts is helpful. Often, it needs to be applied more than once to completely evaluate the integral. Based on the Fundamental Theorem of Calculus Part 2, solving the definite integral over interval[ ]using integration by parts is as follows: ∫ ( ) ( ) [ ( ) ( ) ] ∫ ( ) ( ) Sample Question Evaluate the definite integral using the method of integration by parts. ∫ ( ) √ Solution From the irrational function, the function in the numerator gets simpler as the derivative is taken, but ( ) the function in the denominator does not benefit as much even after the derivative. So let , then ( ) . Then ( ) by chain rule, and . Then, ∫ ( ) √
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