How to Compute the Integral of k(T(x)) from T(x=0) to T(x=L)?

Thread starter andreasgeo
Start date Oct 13, 2013
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Integral

In summary, the "F(g(x))dg(x) integral" is a mathematical notation used to represent the integral of a function composed of two other functions, where the inner function is substituted into the outer function and then integrated with respect to the variable. It is used to simplify the integration process for composite functions. To solve a "F(g(x))dg(x) integral", the inner function is substituted into the outer function and then integration techniques are used. Special cases, such as when the inner function is a constant or the outer function is a trigonometric function, may require different integration techniques.

Oct 13, 2013

andreasgeo

I want to computate the integral:
\int_T(x=0)^T(x=L) k(T(x))\,dT(x)

Anyone can help??

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Oct 13, 2013

mfb

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You can use TeX here:
$$\int_{T(x=0)}^{T(x=L)} k(T(x))\,dT(x)$$

What is k?

1. What is the meaning of "F(g(x))dg(x) integral"?

The "F(g(x))dg(x) integral" is a mathematical notation used to represent the integral of a function that is composed of two other functions. The inner function, g(x), is substituted into the outer function, F(x), and then the resulting function is integrated with respect to the variable, x.

2. What is the purpose of using the "F(g(x))dg(x) integral" notation?

This notation is used to simplify the integration process when dealing with composite functions. It allows us to break down a complex function into smaller, more manageable parts, making the integration process more efficient.

3. How do you solve a "F(g(x))dg(x) integral"?

To solve a "F(g(x))dg(x) integral", we first substitute the inner function, g(x), into the outer function, F(x). Then, we use integration techniques, such as substitution or integration by parts, to integrate the resulting function with respect to the variable, x.

4. Can you provide an example of a "F(g(x))dg(x) integral"?

One example of a "F(g(x))dg(x) integral" is ∫cos(2x)sin(3x)dx. We can rewrite this as ∫sin(3x)d(2x), where the inner function, g(x), is 2x and the outer function, F(x), is sin(3x). Then, we substitute u = 3x and du = 3dx, and the integral becomes ∫sin(u)du, which can be easily solved using integration by parts.

5. Are there any special cases to consider when dealing with "F(g(x))dg(x) integral"?

Yes, there are a few special cases to consider, such as when the inner function, g(x), is a constant or when the outer function, F(x), is a trigonometric function. In these cases, different integration techniques may be needed to solve the integral.