Is it mathematically sound to do this

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In summary, the conversation is about using integration by parts twice, swapping the u and v's, and rearranging the equation to solve for a specific integral. The process is valid and can be used to solve problems involving sines and cosines.
  • #1
brandy
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apply integration by parts twice and swapping the u and v's and then rearranging the equation to say that it is equal to bla/2

like for example i said u is x^n or something and v' is sin x or something.
later on when I am faced with another integral, i apply the int by parts but this time the v' is nx^(n-1) and u is -cos x
then i rearangged the equation to say the initial integral is equal to this...

(these u's and v's are NOT the values i had in the equation AND I REALISE THIS DOESNT WORK HERE, i just want to know if the process is sound. because if so, i will be very happy haha)
 
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  • #2
hi brandy! :smile:

(try using the X2 icon just above the Reply box :wink:)

yes that's perfectly valid

for example ∫ sinnx dx = [-cosx sinn-1x dx] + (n-1)∫ cos2x sinn-2x dx …

use cos2 = 1 - sin2, and put like terms together :wink:
 

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Yes, mathematical concepts are an integral part of scientific research as they provide a structured and logical framework for analyzing data and making predictions. Without mathematics, it would be difficult to quantify and explain complex phenomena.

2. What is the importance of mathematical soundness in scientific experiments?

Mathematical soundness ensures that the results of a scientific experiment or study are accurate and reliable. It helps to eliminate errors and biases, and allows for proper interpretation and replication of the results.

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5. Are there any limitations to using mathematics in scientific research?

While mathematics is a powerful tool in scientific research, it is not suitable for all types of studies. Some phenomena may be too complex to be accurately represented by mathematical models, and in such cases, alternative methods may need to be used.

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