∫(- 2→- 1) √(3 - 4x - x^2) dx
= ∫(- 2→- 1) √[7 - (x + 2)^2] dx
x + 2 = √7sinθ、dx = √7cosθ dθ
θ∈[0,arcsin(1/√7)]
= ∫ (√7cosθ)(√7cosθ) dθ
= 7∫ cos^2(θ) dθ
= (7/2)∫ (1 + cos2θ) dθ
= 7θ/2 + (7/2)sinθcosθ
= (7/2)arcsin(1/√7) + (7/2)[(1/√7)√(1 - 1/7)]
= (7/2)arcsin(1/√7) + √6/2