Trigonometric Integrals by Substitution

awsalazar
Messages
2
Reaction score
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
 

Attachments

  • Trig Integral.jpg
    Trig Integral.jpg
    19.8 KB · Views: 501
Last edited:
Physics news on Phys.org
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.
 
I don't see an error, and I can confirm that your solution is correct.
 
Thanks a lot guys, and good advice Karnage1993, a much easier process then what I was doing.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top