Math Is Fun Forum

I have recently just learned about substitutions with trig functions for the function in the title. I'm not sure as to how to get the function back to a state of X instead of a cosθ  or sin θ . If anyone knows anything about that, Please help me understand it. Thanks

Actual problem in my book.

∫√ (2^2-x^2)

x = asinθ
dx = acosθDθ

= ∫2cosθDθ√ (4-4sin^2θ)dθ
= ∫2cosθDθ√ (4[1-sin^2θ])dθ
= ∫2cosθDθ√ (4cos^2θ)dθ
= ∫2cosθDθ2cos θdθ
= ∫4cos^2θDθ