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.

Separable differential equation

2.1.1.23] Solve




Solution:














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[Reference: 5]

Real life {*_*}

It is only two weeks into the term that, in a calculus class, a student raises his hand and asks: "Will we ever need this stuff in real life?"

The professor gently smiles at him and says: "Of course not - if your real life will consist of flipping hamburgers at MacDonald's!"

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Source:

[2]

A drink too many

A cone-shaped paper drinking cup is to be made to hold 27 cu cm of water. Find the height and radius of the cup that will use the smallest amount of water. [4]

This is one of the problems which, by taking the usual road, can make the solution more complicated than the problem.

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Source:

[4]
Problem 36, page 338.

Horseplay {*_*}

A mathematician and a stock broker go to the races to bet on horses. The broker suggests a bet of $10,000. That's too much for the mathematician's taste: First, he wants to understand the rules, have a look at the horses, etc.


"Don't worry", the broker says. "I know an empirical algorithm that allows me to find the number of the winning horse with absolute certainty."


This does not convince the mathematician.


"You are too theoretical!" the broker exclaims and puts his $10,000 on a horse.
The horse comes in first - making the broker even richer than he already is. The mathematician is baffled.


"What is your algorithm?" he wants to know.


"It's rather easy. I have two children, three and five years old. I add up their ages and bet on that number."


"But three plus five is eight - and that horse had number nine!"


"I told you that you're too theoretical! Didn't I just experimentally prove that my calculation is correct?!"


Source:


[2]