∫√(1-x^2 ) dx
Letting x = sin θ,
dx/dθ = cos θ
∫√(1-x^2 ) dx
=∫√(1-sin^2θ ) cos θ dθ
=∫cos^2 θ dθ
=∫ (1-sin^2θ) dθ
=θ -2sinθ(-cosθ) + c
=θ +2sinθcosθ + c
=sin^(-1)θ + 2x√(1-x^2 ) + c
Is this correct? Please help me to check whether it is correct or not, and point out my mistake, if any. Thank you.