Trigonometric Integrals by Substitution

In summary, the conversation discusses the integration of the integral ∫((sin(√x))^3*dx)/√x and the use of a TI-Nsprire CAS to check for errors. The individual's solution is confirmed to be correct and they receive advice on how to easily check for errors in the future.
  • #1
awsalazar
2
0
I am unsure whether I have properly performed the integration of the integral ∫((sin(√x))^3*dx)/√x

When I used my TI-Nsprire CAS to take the derivative of my answer in order to check if I was correct, and it came out differently. Now I used some trig identities to manipulate the problem, so I figured that is why it was different. So when I stored the integral into one function and the solution into another function, values I would enter were different for each function. Can someone correct any errors I have made or confirm that my answer is correct?

I have attached my attempt at the integral as a .jpg file.
∫((sin(√x))^3*dx)/√x
 

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  • #2
Your solution and answer are correct. Note that whatever answer your calculator had, you can merely subtract it from the original and see if the result is 0.
 
  • #3
I don't see an error, and I can confirm that your solution is correct.
 
  • #4
Thanks a lot guys, and good advice Karnage1993, a much easier process then what I was doing.
 

FAQ: Trigonometric Integrals by Substitution

What is the purpose of using substitution in trigonometric integrals?

Substitution allows us to transform a complicated integral involving trigonometric functions into a simpler one that can be easily solved using basic integration techniques.

How do you choose the substitution in a trigonometric integral?

The substitution should be chosen based on the trigonometric function present in the integral. For example, if the integral contains a sine function, we can use a substitution of u = cos(x) to transform it into an integral involving only cosine.

Can any trigonometric integral be solved using substitution?

No, substitution is only effective for certain types of integrals involving trigonometric functions. It may not be useful in cases where the integral involves complicated expressions or multiple trigonometric functions.

What are some common mistakes to avoid when using substitution in trigonometric integrals?

One common mistake is to forget to substitute back to the original variable at the end of the integral. Another mistake is to use the wrong substitution or to apply it incorrectly, resulting in an incorrect solution.

Are there any other methods for solving trigonometric integrals besides substitution?

Yes, there are other methods such as integration by parts and the use of trigonometric identities. The choice of method often depends on the complexity of the integral and the trigonometric functions involved.

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