Integration using Tables of Integrals: Example 1

in mathematics •  3 months ago  (edited)

In this video I go over the use of tables of integrals when integrating functions. Integration using tables of integrals has been widely used in the past before the internet was fully developed and integration computer algebra systems (CAS) were widely available online. That being said they are useful when you don't have an CAS available or your internet connection is not working. In this video I go over the example of finding the volume of the region bounded by the functions y = arctan(x), y = 0 and x = 1 and rotated about the y-axis. The problem involves solving an integral with an integrand of the form u*arctan(u). Luckily the integral of such an integral can be found in formula number 92 in the Table of Integrals found in my calculus book as well as through this link: https://tinyurl.com/integralsmes.


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Integration using Tables of Integrals: Example 1

Integration Tables Example 1.jpeg

Tables of indefinite integrals are very useful when we are confronted by an integral that is difficult to evaluate by hand and we don't have access to a computer algebra system (CAS); in other words, in the case we don't have internet access as there are many online CAS calculators

I will be using the Table of Integrals found in my calculus book and you can view that table by going to the URL: https://tinyurl.com/integralsmes

It should be remembered that often times that integrals do not occur exactly in the form listed in a table.

  • Usually we need to use substitution or algebraic manipulation to transform a given integral into one of the forms in the table.

Example 1:

The region bounded by the curves y = arctan(x), y = 0, and x = 1 is rotated about the y-axis. Find the volume of the resulting solid.

Solution:

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