A complicated integral

  • Thread starter ARYT
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    Integral
In summary, an integral is a mathematical concept used to calculate the area under a curve on a graph. A complicated integral is difficult to solve and may involve multiple variables or non-standard techniques. To solve a complicated integral, one can use techniques like substitution, integration by parts, or numerical methods. These integrals are important in various fields of science and can have multiple solutions due to different approaches and indefinite solutions.
  • #1
ARYT
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Homework Statement



My answer should not be correct. Right?:uhh:
Refer to the attachment please.

Homework Equations



Refer to the attachment please.

The Attempt at a Solution



Refer to the attachment please.

Cheers
 

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  • #2
Why not do a partial integration?

x/sqrt[x^2+1] * x^2 dx

You can integrate x/sqrt[x^2+1] this is proportional to
sqrt[x^2+1]

So, if you do a partial integration, you'll have to deal with the integral:

x sqrt[x^2+1]

where the x comes from the derivative of x^2. But this is then proportional to (x^2+1)^(3/2).
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to calculate the total value of a function over a specific interval.

2. What is a complicated integral?

A complicated integral is an integral that is difficult to solve due to its complexity. It may involve multiple variables, functions, or non-standard integration techniques.

3. How do you solve a complicated integral?

To solve a complicated integral, you can use various techniques such as substitution, integration by parts, or numerical methods like Simpson's rule. It may also require advanced mathematical knowledge and problem-solving skills.

4. Why are complicated integrals important?

Complicated integrals are important in various fields of science, including physics, engineering, and economics. They are used to model real-world problems and make predictions by finding the total value of a function over a specific interval.

5. Can a complicated integral have more than one solution?

Yes, a complicated integral can have multiple solutions. This is because there are many different approaches and techniques that can be used to solve an integral, and each one may yield a different result. Additionally, some integrals may have indefinite solutions, meaning that they can be expressed in multiple forms.

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