[QUOTE=skeeter;461233]other than recognizing that the area of a semicircle is , no.
So if I am allowed to recognize that the area of the semicircle is as above....
how could I integrate y=sqr r^2-x^2
without using substitution?
Calculus makes frequent use of trigonometric identities, which SHOULD (but aren't always) be covered prior to taking the course. If you are not familiar with them then here is a site for them:
wolfound, you will benefit greatly by strengthening your trig skills. that substitution, , can be derived from the manifest identity and the angle sum formulas as derived, and proven geometrically here:
The Sine of the Sum of Angles
this website even has a drill section with solutions, so you can test your skills once you study their modules.