- #1

Bashyboy

- 1,421

- 5

## Homework Statement

I am doing a little review and having a some trouble deriving the integral ##\int \frac{1}{\sqrt{1-x^2}} dx##

## Homework Equations

## The Attempt at a Solution

Initially I was trying to solve this integral using the substitution ##\cos \theta = x##. I drew my triangle so that the side adjacent to ##\theta## was ##x##, the hypotenuse was ##1##, and from this found that the opposite side was ##\sqrt{1-x^2}##; after this I computed my differentials, performed various substitutions, and concluded that ##\int \frac{1}{\sqrt{1-x^2}} dx = - \arccos x + c##. However, this wrong. So, I tried the substitution ##\sin \theta = x## and I derived the correct formula. Why didn't my first substitution work?