- #1
msmith12
- 41
- 0
this integral was on a test I took recently--any thoughts or ideas on how to attack it?
[tex]
\int_{0}^{1} \frac{x\sin{x}}{1+\cos^2{x}}dx
[/tex]
~matt
[tex]
\int_{0}^{1} \frac{x\sin{x}}{1+\cos^2{x}}dx
[/tex]
~matt
TheDestroyer said:BobG, You're integration isn't correct, You did 2 opposite partitions in 1 integral, the integration of [tex]arctan(cos(x))[/tex] isn't correct, and it's not possible to be integrated
dextercioby said:What's Mupad...?
This was on a test? My first impression was that this has to be an easy problem if you just look at it the right way. I keep thinking you definitely want the arctangent, arcosine, or arcsine since your limits of integration are 0 to 1 (they would work out very nicely). But the problem just doesn't work nicely at all. Did the teacher make a typo?msmith12 said:this integral was on a test I took recently--any thoughts or ideas on how to attack it?
An integral is a mathematical concept that represents the area under a curve in a given interval. It is a fundamental concept in calculus and is used to solve problems involving rates of change, such as velocity and acceleration.
"Yet another interesting integral" is a phrase that is often used to introduce a particularly challenging or intriguing integral problem. It can also refer to integrals that have unique and interesting solutions, or those that have real-life applications.
The method for solving "Yet another interesting integral" will depend on the specific problem and the techniques and formulas that are applicable to it. Generally, the first step is to identify the type of integral (e.g. definite or indefinite) and then use techniques such as substitution, integration by parts, or partial fractions to solve it.
One example of "Yet another interesting integral" is the integral of the logarithm function, ∫ ln(x) dx. This integral has a unique solution that involves the natural logarithm and is often used in physics and engineering to solve problems involving exponential growth and decay.
Integrals play a crucial role in many scientific fields, including physics, engineering, and economics. They allow us to calculate quantities such as area, volume, and work, which are essential in understanding and predicting real-world phenomena. Integrals also help us to model and analyze continuous processes, making them a powerful tool for scientific research and problem-solving.