Simple question about direct integration

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In summary, direct integration is a mathematical technique used to find the antiderivative of a function by reversing the process of differentiation. Unlike other integration methods, it relies on recognizing the derivative of a function and does not require a specific formula or rule to be applied. The steps involved in direct integration include rewriting the function, determining the antiderivative, and adding a constant of integration. It is typically used when the function has a recognizable derivative and other methods are not applicable. Some common mistakes to avoid when using direct integration include forgetting to add the constant of integration, confusing derivatives with inverses, using incorrect techniques, and not simplifying the final solution.
  • #1
Tuneman
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if I have a equation like this

img239.gif

I know I can integrate so that
img240.gif


but this does not make sense to me because I could think of many U's that if you were to take the derivitive with respect to the squiggly varibale, still includes both variables
 
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  • #2
If the derivative with respect to xi includes both variables, then how does it look when you differentiate with respect to both xi and to eta?
 
  • #3
http://www.threepointstance.net/tpsbb/images/smilies/clever.gif
 
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FAQ: Simple question about direct integration

What is direct integration?

Direct integration is a mathematical technique used to find the antiderivative of a function. It involves reversing the process of differentiation to find the original function from its derivative.

How is direct integration different from other integration methods?

Direct integration is also known as the primitive method or the method of integration by inspection. Unlike other integration methods, it does not require a specific formula or rule to be applied, but instead relies on recognizing the derivative of a function and working backwards to find the original function.

What are the steps involved in direct integration?

The steps involved in direct integration include: 1) rewriting the given function in its derivative form, 2) determining the antiderivative of the function by reversing the derivative process, and 3) adding a constant of integration to the antiderivative to account for all possible solutions.

When should direct integration be used?

Direct integration is typically used when the function to be integrated has a recognizable derivative. It can also be used when other integration methods are not applicable or too complex to be used.

What are some common mistakes to avoid when using direct integration?

Some common mistakes to avoid when using direct integration include: 1) forgetting to add the constant of integration, 2) confusing the derivative of a function with its inverse, 3) using incorrect substitution or integration techniques, and 4) not simplifying the final solution.

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