- #1
Doom of Doom
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[tex]\int_{0}^{2\pi} \frac{dx}{1+e^{sin(x)}}[/tex]
How would you evaluate this integral? Where do you even start?
How would you evaluate this integral? Where do you even start?
hotcommodity said:Well, we know that [tex]\int \frac{dx}{1 + x^{2}} = arctan(x) + C [/tex].
How can we think of [tex] e^{sin(x)} [/tex] as a term that's been squared?
Doom of Doom said:[tex]\int_{0}^{2\pi} \frac{dx}{1+e^{sin(x)}}[/tex]
How would you evaluate this integral? Where do you even start?
A "Crazy integral" is a term used to describe a particularly complex or challenging mathematical integral that may involve unusual functions, techniques, or substitutions.
"Crazy integrals" are important because they often represent real-world problems that require advanced mathematical techniques to solve. By studying these integrals, scientists can develop new methods and techniques to solve complex problems in various fields such as physics, engineering, and finance.
When faced with a "Crazy integral", it is important to first understand the properties and behavior of the functions involved. Then, different techniques such as integration by parts, trigonometric substitutions, or partial fractions can be applied to simplify the integral. Practice and persistence are key to successfully solving these challenging integrals.
Yes, "Crazy integrals" can be solved by hand using various mathematical techniques. However, for extremely complex integrals, it may be necessary to use computational methods or software to obtain an approximate solution.
Some tips for solving "Crazy integrals" include breaking the integral into smaller, more manageable parts, using symmetry or other patterns to simplify the problem, and being creative with substitutions or transformations. It is also helpful to have a strong understanding of mathematical concepts and techniques, and to practice solving a variety of integrals.