Choosing the correct method of integration.

In summary, the proper method for integration can be either by parts or by substitution. If the correct answer is obtained through an obscure method of substitution, it should also be obtained through integration by parts. However, if different methods yield different answers, there may be an error in one of the methods or the results may just be different expressions of the same thing. The preferred method is the easiest one that yields the correct result, regardless of the method used.
  • #1
eliwood1221
1
0
Hey, i am just wondering how one chooses whether the proper method for integration is by parts, or by substitution. if by some OBSCURE method of substitution gives me the correct answer, will integrating by parts give the same? for example
INTEGRAL 2t/((t-3)^2) dt. i used a parts substitution first, and got one answer, but it is different than other answers generated by substitution..
 
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  • #2
If you integrate correctly, no matter the method of integration, then your answer will always be the same, up to a constant. Perhaps you can show your work so we can try to figure out where you may have gone wrong?
 
  • #3
The preferred method is the easiest one that gets the job done. It does not matter what method you use, if applied properly the result will be the same. If you do not get the same result with different methods you have made an error in one or the other. You also might want to check that your results are just different expressions of the same thing.
 

FAQ: Choosing the correct method of integration.

What is the purpose of choosing the correct method of integration?

Choosing the correct method of integration allows for efficient and accurate mathematical computations, allowing scientists to accurately model and understand complex systems in a variety of fields such as physics, chemistry, and engineering.

How do I determine which method of integration to use?

The method of integration chosen depends on the specific function being integrated and the goal of the integration. Some common methods include substitution, integration by parts, and partial fractions. It is important to consider the properties of the function and choose a method that best suits the problem at hand.

What are some common mistakes made when choosing a method of integration?

One common mistake is not understanding the properties of the function being integrated and choosing an incorrect method. Another mistake is not carefully checking the algebraic manipulations involved in the integration process, which can lead to incorrect results.

Are there any tools available to help with choosing the correct method of integration?

Yes, there are various online calculators and software programs that can help with choosing the appropriate integration method for a given function. Additionally, consulting with a mathematics expert or utilizing integration tables can also aid in selecting the correct method.

Can the choice of integration method affect the accuracy of the results?

Yes, the choice of integration method can have a significant impact on the accuracy of the results. Using an incorrect method or making mistakes during the integration process can lead to incorrect solutions. It is important to carefully choose and execute the appropriate method to ensure accurate results.

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