- #1
epkid08
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- 1
I really have no idea how to do this, please show some steps.
[tex]\int arg(x^{ix} + x^{-ix}) dx [/tex]
[tex]\int arg(x^{ix} + x^{-ix}) dx [/tex]
Dick said:If x is real the exp(ix)+exp(-ix) is real. Why? What is arg of a real number? Are you sure that's the whole problem?
Integral Help refers to assistance or guidance in solving integrals, which are mathematical expressions that represent the area under a curve. It is a common topic in calculus and is used to solve various problems in physics, engineering, and economics.
Solving this integral involves using the substitution method, specifically the substitution u = x^{ix} + x^{-ix}. By using this substitution, the integral can be rewritten as \int arg(u) du, which can then be solved using integration by parts or other techniques.
The variable x^{ix} + x^{-ix} is known as a complex number, which is a number that has both a real and imaginary component. In this integral, it is used to represent the function being integrated, and its complex nature allows for a more challenging problem to be solved.
Yes, this integral can be solved without using complex numbers by using the substitution u = e^x. This leads to an integral that can be solved using standard integration techniques.
This integral is important in mathematics because it involves complex numbers, which have many applications in various fields. It also requires a combination of different integration techniques, making it a challenging problem to solve and a good exercise for students learning calculus.