Unit 7A

Integrals Part 1

Lesson 6: Integration by Parts

So far, most of the material presented in this Unit involving integrals has used derivatives as a starting point. Continuing in this direction, consider the product rule «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»d«/mi»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mi»u«/mi»«mi»v«/mi»«mo»=«/mo»«mi»u«/mi»«mfrac»«mrow»«mi»d«/mi»«mi»v«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mi»v«/mi»«mfrac»«mrow»«mi»d«/mi»«mi»u«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/math». Try integrating both sides of the equation. Might the result contribute to a technique for integrating a product?