Integration Techniques: Problems 2.1.27.23 and 2.1.29.23

Obtain the general solution for the following problems:

2.1.27.23]


2.1.29.23]

Obviously, trigonometric identities will come into play here. Problems like these will be covered in the integration techniques workshop.


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Reference: [5]

Mathematics

Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.

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Reference: [7]

Integration Techniques: Problem 3.17.21

Problem 3.17.21] Solve



This is one of the problems which looks intimidating because of its form. A simple technique can solve this although one approach is superior than the other.


We'll solve this in the workshop.

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Reference: [6]

Book: Fermat's Last Theorem

This is an immensely enjoyable treasure.

[image source: Amazon.com. 2009. Fermat's Last Theorem. http://ecx.images-amazon.com/images/I/51WX45QBQBL._SL500_AA240_.jpg. Last accessed: Oct 9, 2009.]

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Integration Techniques: Problem 3.14.20

Here's another problem which requires some integration.

Problem 3.14.20] Solve


Can you identify what technique will work for this kind of problem?


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Reference: [6]

Integration techniques: Problem 3.7.17.17

Problem 3.7.17.17] Solve

If you can solve this problem, maybe you should join me. I will offer a workshop on integration techniques soon. I am just finishing my workbook which contains:

1] Introduction. What basic weapons do you need to tackle integration problems? What areas will you find integration techniques useful?

2] Integration Techniques. By merely looking at the problem, how do you know which technique is applicable and will most likely work?

3] Problems. What are the various kinds of inegration problems? At least 10 problems will be given for each kind.

4] Solutions. Detailed solutions will be given. Alternative approaches will also be presented.

5] References.

My workbook is about 1/3 done. For now, I will post my selected problems.

You can join me in at least two capacities. First, you can serve as facilitator in workshops. Second, you can attend as a student. Third, you can donate funds.

The workshops will be held in series, ideally throughout the Philippines, wherever we are needed. This integration technique workshop is actually just one of the many activities I have in mind for the Lemniscate Engineering Institute. We will package programs and projects for this entity and hopefully, we can get sustained external funding.

In the past, we're just offering the Lemniscate Prize which is a monetary reward for undergraduate research in agricultural engineering and food technology. This is already on its 3rd year. This time, we're expanding. We'll build a library and we'll offer workshops. For the library, we already have about a dozen titles in mathematics, physics, agricultural engineering and food engineering.

We're doing this for many reasons. For one, I think we need more engineers and scientists than politicians.

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In search of Schrodinger's cat

I finished reading this last month. Nothing spectacular. Good enough for leisurely reading.