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Lv 5
Integration troubles?
∫ √(1-x²) dx
I know that you're supposed to set x = sin(u), but why would you do that?
1 Answer
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- Alam Ko IyanLv 71 decade agoFavorite Answer
that is the effective technique to solve the integral
x = sinu
dx = cosu du
integral becomes
∫ cos^2u du
= 1/2 ∫ (1 + cos(2u)) du
= 1/2 u + 1/4 sin(2u) + C
= 1/2 arcsin(x) + 1/2 x √(1-x²) + C
whenever there is a quadratic with radicals involved, trigonometric substitution is the effective approach
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