Hi guys. I'm trying to find the measure of a given angle without using the trig functions. I have devised an equation that I believe will do the trick but I don't know how to integrate (r^2-x^2)^1/2 where the value r^2 is constant. Can anyone please show me how it's done. Thanx.

How do you integrate the equation of a circle? (with y positive so that we are dealing with a function not a relation)

Imagine in your mind a circle in standard position with radius r. Now r has traveled (starting at the x-axis) around the circle such that r forms an angle with the x-axis between 0 and 90 degrees. I am trying to find the area bounded by the segment (x-r), the length of the y ordinate, and the arc that is formed beginning a x and traveling to y.

How do I do this. Look again at my problem above.

Make the substitution

I'm trying to do this without the trig functions! I'm sick of that stupid one-to-one correspondence and all of the tables. How the heck does a calculator do it?