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lioric
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I cannot understand the intergration done here
The part how 1/a came, what happened to the x and how did tan come into this
The x went away because it is the dummy integration variable in a definite integral.lioric said:View attachment 96316
I cannot understand the intergration done here
The part how 1/a came, what happened to the x and how did tan come into this
Samy_A said:The x went away because it is the dummy integration variable in a definite integral.
For starters: do you know how to evaluate the following indefinite integral: ##\int \frac{1}{1+x²}dx##?
Do you know how to use a substitution in order to compute an integral?lioric said:No
Samy_A said:Do you know how to use a substitution in order to compute an integral?
Fine. So start with the indefinite integral ##\int \frac{1}{1+x²}dx## and use the substitution ##x=\tan y## to compute it.lioric said:Yes
Thank you very muchSamy_A said:Fine. So start with the indefinite integral ##\int \frac{1}{1+x²}dx## and use the substitution ##x=\tan y## to compute it.
You can do it in two (very similar) ways.lioric said:View attachment 96332
This was as far as I could go
I'm wondering how that 1/a came and how to make this into a 1/x^2+1 formate so I can input tan
Please help
The integration of 1/(x^2 + a^2) refers to the process of finding the antiderivative of the function 1/(x^2 + a^2). This involves finding a function whose derivative is equal to 1/(x^2 + a^2).
The integration of 1/(x^2 + a^2) is important in mathematics, physics, and engineering as it allows us to solve a wide range of problems involving the area under a curve or the accumulation of a quantity over time.
There are several methods for integrating 1/(x^2 + a^2), including substitution, partial fractions, and trigonometric substitution. The choice of method depends on the form of the function and the desired simplicity of the solution.
The integration of 1/(x^2 + a^2) has many applications in physics, such as calculating the electric potential of a point charge, the gravitational potential of a point mass, or the magnetic field of a current-carrying wire. It is also used in engineering for solving differential equations and in economics for calculating the present value of a continuous cash flow.
There is no single formula for integrating 1/(x^2 + a^2) as the answer depends on the value of a and the chosen integration method. However, there are tables of integrals that provide specific solutions for certain values of a and different methods of integration.