Integrate $\int x^2\sin^{-1}\left ( \frac{\sqrt{a^2-x^2} }{b} \right ) dx$ 

I have  already done some progress for this integral at mathexchange

The objective is to compute the following definite integral:

$\int^w_0 x^2\sin^{-1}\left ( \frac{\sqrt{a^2-x^2} }{b} \right ) dx$

Once the indefinite one is done you can easily proceed with the limits. The constants $a$ and $b$ are non-zero positive, and $x<a$.

Integrals Calculus
Rf S Rf S
8
Report
  • Rf S Rf S
    0

    I do not want a complex form such as the one from Wolfram Alpha. I need the working out of it too.

Answer

Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer

1 Attachment

Erdos Erdos
4.7K
  • Erdos Erdos
    0

    Please leave a comment if you need any clarifications.

  • Rf S Rf S
    0

    Thank you Philip for the response. Sorry in advance if I sound ignorant (I am haven't got much knowledge on these elliptic integrals). Can the result $I(x)$ from the Wolfram Alpha page be plotted in a graph? (provided a and b).

  • Erdos Erdos
    0

    Yes, you may graph them by Matlab: https://www.mathworks.com/help/matlab/ref/ellipke.html

  • Erdos Erdos
    0

    All functions appearing in the formula are basic, all you need is to be able to graph the elliptic integrals of first and second kind.

The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.