6.1 Integration by Parts; Integration Tables

This technique is based on the product rule for derivatives.

Traditional Integration by Parts

The text has steps listed in a table on page 465 

When to Use: If the integral is a product where one of the factors can be easily integrated and the other factor can be easily differentiated.

”The Challenge”   Choose the appropriate u and dv

Which technique??   

Compare and Contrast - Parts vs. Substitution

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Application

#42 A manufacturer has found the marginal cost is dollars per unit when q units have been produced. The total cost of producing 10 units is $200. What is the total cost of producing the first 20 units?

#40 Find the function whose tangent line has slope for each value of x>0 and whose graph passes through the point (2,-3)

Table of Integrals – Pages 484-485

Repetitive Formulas

(**shortcut easier**)

Recognizing different types of integration

Assignment 6.1 – page 487 – 1-23 odd, 27-43 odd, 47