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Orion1
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Is it possible to integrate a trigonometry function within a function, or is this a formula that cannot be integrated in terms of elementary functions?
[tex]\int \sin(\cos x) dx[/tex]
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Plastic Photon said:If sin(x)=y and arcsin(y)=x , why can sin(arcsiny) not be integrated with elementary function? It is equivalent to integrating sin(x) which is -cosx + C, correct? So why is sin(cosx) any different, does this not apply to inverse trig functions?
Orion1 said:Here is the theorem that I developed for any trig function within a function:
[tex]\int u[v(x)] dx = u [ \int v(x) dx ] + C[/tex]
What do you mean by "refuted"? Did you read Matt Grimes post? Perhaps if you did not understand it you should make an effort to. What is means is that your function is fine, and an integral exists. But as others have said the integral cannot be expressed in terms of elementary functions.Orion1 said:
I retract my term 'theorem', perhaps I should have used the term pseudo-developmental philosophy...
Please post a graph of what F(x) appears like versus f(x)?
[tex]f(x) = \sin(\cos x)[/tex]
[tex]\int \sin(\cos x) dx = F(x) + C[/tex]
I would post my graphs for f(x) = Sin (Cos x) and F(x) = Sin (Sin x), however these functions have been refuted here.
The graph for F(x) can be drawn or graphed manually, can it not?
Cos(x) ~ x + (x^2)/2 + ...
[tex]\int {\tan x\,dx} = \int {\frac{{\sin x}}xerobeatz said:hi, I am new here, can i ask how 2 integrate "tan x"
Orion1 said:
I retract my term 'theorem', perhaps I should have used the term pseudo-developmental philosophy...
Trigonometric integration is the process of finding the integral of a function that contains trigonometric functions, such as sine, cosine, or tangent.
Trigonometric integration is important in many areas of mathematics, physics, and engineering. It allows us to solve complex problems involving periodic functions and is essential in calculating areas, volumes, and other physical quantities.
The integration of trigonometric functions follows specific rules and techniques, such as using trigonometric identities, substitution, and integration by parts. It also requires a good understanding of basic calculus concepts like derivatives and antiderivatives.
Trigonometric integration has various applications in fields such as engineering, physics, and mathematics. Some common examples include calculating the period and frequency of oscillating systems, determining the displacement and velocity of a particle undergoing circular motion, and finding the center of mass of a rotating object.
Some useful tips for solving trigonometric integration problems include identifying the appropriate trigonometric identities to simplify the integrand, using trigonometric substitution to transform the integral into a more manageable form, and practicing regularly to improve problem-solving skills.