Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b))

over 4 years ago (Edited)

In this video I go over an interesting section in my Calculus book called Discovery Project and go over Question 1 of the Patterns in Integrals project. The Discovery Project section explores specific topics in calculus in greater detail. In this video I use a Computer Algebra System (CAS) to go over the family of functions in the form of the integral of 1/((x+a)(x+b)) and show how we can derive the general integral formula by using a CAS to determine answers to different examples and finding the pattern in the answers. I also go over the solution by hand using the method of partial fractions to double check that the CAS formula guessing method is correct, which indeed it is. This is a very important video as it shows the power of computers to derive formulas for entire families of integrals so make sure to watch this video!

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Discovery Project: Patterns in Integrals: Question 1

Discovery Project Integral Patterns Question 1.jpeg

This is part of a section in my calculus book called "Discovery Project" which explores specific topics in calculus in greater detail.

In this project a computer algebra system (CAS) is used to investigate indefinite integrals of families of functions. By observing the patterns that occur in the integrals of several members of the family, we will be able to first guess, and then prove, a general formula for the integral of any member of the family.