- #1
jamesd2008
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Hi, what result do you get if you intergrate Inx with respect to x?
Thanks
James
Thanks
James
Intergrate Inx with respect to x?
- Thread starter jamesd2008
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In summary, integration with respect to x is a mathematical process used to calculate the value of a function by finding the area under the curve of the function with respect to the variable x. It is different from integration with respect to other variables, as the variable of integration is the independent variable in this case. The purpose of integrating with respect to x is to find the value of a function at a specific point or over a given interval, and it has various applications in math, science, and economics. Integration with respect to x can also be used for functions with multiple variables through partial integration, and it has real-world applications in physics, engineering, geometry, economics, and statistics.
- #2
tiny-tim
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jamesd2008 said:
Hi James!
(i assume you mean "lnx")
Hint: integration by parts
- #3
jamesd2008
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As in the opposite of exponential.
Thanks
James
- #4
HallsofIvy
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First, it is ln(x), not "In(x)"!
As tiny-tim suggested, use integration by parts. That might seem strange since there is only one "part" but let u= ln(x) and dv= dx and every thing works out nicely.
- #5
jamesd2008
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Ok, thanks for your replies, james.
FAQ: Intergrate Inx with respect to x?
What is integration with respect to x?
Integration with respect to x is a mathematical process where the value of a function is determined by calculating the area under the curve of the function with respect to the variable x. It is a fundamental concept in calculus and is used in many areas of science, engineering, and economics.
How is integration with respect to x different from integration with respect to other variables?
The main difference between integration with respect to x and other variables is the variable of integration. When integrating with respect to x, the variable x is the independent variable, and the function is integrated with respect to it. In other types of integration, such as integration with respect to y or z, the variable of integration is different, and the function is integrated with respect to that variable.
What is the purpose of integrating with respect to x?
The purpose of integrating with respect to x is to find the value of a function at a given point or over a specific interval. It is also used to calculate the area, volume, and other quantities in various mathematical and scientific applications.
Can integration with respect to x be used for functions with multiple variables?
Yes, integration with respect to x can be used for functions with multiple variables. In this case, the other variables are treated as constants, and the integration is performed solely with respect to x. This is known as partial integration and is commonly used in physics and engineering.
What are some real-world applications of integration with respect to x?
Integration with respect to x has many real-world applications, including calculating the area under a curve in physics and engineering problems, determining the volume of irregular shapes in geometry, and finding the total cost or revenue in economics. It is also used in statistics and probability to calculate the probability distribution of a random variable.