Question about Legendre elliptic integrals

In summary, the conversation discusses an example from a study material where the first step involves using the substitution method to solve an integral. The person is unsure about why this step was chosen and expresses concern about relying on "educated guesses" in math. The conversation ends with a humorous reference to the discovery of the new world and a joke about being "devoured by the Kraken."
  • #1
mercenarycor
6
0

Homework Statement

[/B]
J(a, b, c;y)=∫aydx/√((x-a)(x-b)(x-c)), let a<b<c

Homework Equations


f(θ, k)=∫0θdx/√(1-k2sin2(x)), k≤1

The Attempt at a Solution


This is an example from my study material, and I don't understand the first step they do.
Let x=a+(b-a)t, dx=(b-a)dt
Wait...what? Why? How did they come to that decision. I hope there's a logical reason, otherwise how can I apply this to my other problems? I keep running into "make an educated guess." Is this another guess?
 
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  • #2
I suggest you show a bit of unquestioning blind faith and try it.
 
  • #3
And that is how we discovered the new world!
 
  • #4
And that is how we discovered the new world!

No shipwrecks or monstrous squid, I take it?
 
  • #5
Devoured by the Kraken, I'm afraid. Ended up dropping the course, going to spend the summer with Schaum's trying to build a better foundation for the math I need.
 

1. What are Legendre elliptic integrals?

Legendre elliptic integrals are a type of mathematical function that arise in the study of elliptic curves and elliptic functions. They are named after the French mathematician Adrien-Marie Legendre who first studied them in the late 1700s.

2. What is the purpose of Legendre elliptic integrals?

Legendre elliptic integrals are used to calculate the arc length, perimeter, and area of an ellipse. They also have applications in physics, engineering, and other fields of science.

3. How are Legendre elliptic integrals different from other types of integrals?

Legendre elliptic integrals are different from other types of integrals because they involve the integration of rational functions of the form √(P(x)/Q(x)), where P(x) and Q(x) are polynomials. This makes them more complex and challenging to evaluate.

4. Are there different types of Legendre elliptic integrals?

Yes, there are three main types of Legendre elliptic integrals: the first, second, and third kind. Each type is denoted by a different symbol and has different properties and applications.

5. How are Legendre elliptic integrals used in real-world problems?

Legendre elliptic integrals have many practical applications, such as in calculating the period of a pendulum, the motion of a planet around the sun, and the bending of a beam under load. They are also used in the fields of astronomy, geodesy, and celestial mechanics.

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