2
$\begingroup$

What is the integral $$\int \arccos(z/\sqrt{R^2-x^2})dx$$

This is one of 4 equations for integrating the area of a major sector of a circle within a sphere between limits to find its volume. Two of the functions are easily integrated (first and last), but the above and $\int\arccos(x^2(z/\sqrt{R^2-x^2}))dx$ are difficult to do. I also need the integration of this equation too.

The full equation to be integrated is: $$ Area = \pi(R^2-x^2)-(R^2-x^2)\arccos(z/\sqrt{R^2-x^2}+z*\sqrt{R^2-x^2-z^2}. $$ The function $z$ is the distance to the major segment chord from the center.

  • 0
    Try substituting $x = R \cos \theta$ (or $\sin$).2012-10-01
  • 0
    It's not clear exactly what you're trying to compute, but it's likely there's a much easier method than this.2012-10-01

1 Answers 1