Question

What is the integral of `sqrt(1-x^2)`?

Answer 1

Hint: First, apply trigonometric substitution. This question is in the form `sqrt(a^2-x^2)`. So you let x = a sinx (a in this case is 1) then take the derivative of x. Plug it back in the question `int sqrt(1-x^2) dx`
You will have to use the half-angle identity after.
Integrate. You will get an indefinite integral.
Set up a right triangle to find the value for the indefinite integral.

I hope this video would help clear things up.