09/10/03 07:06:14
>>784
S(a) = S_1(a) + S_2(a) - S_3(a),
S_1(a) = ∫[-a, -a/(1+a)] (-ax)dx = [ (-1/2)ax^2 ](x=-a, -a/(1+a)) = (2+a)(a^4)/{2(1+a)^2},
S_2(a) = ∫[-a/(1+a),0] { a-x-2√{a(-x)(x+1)} } dx
= [ ax -(1/2)x^2 -(x +1/2)√{a(-x)(x+1)} + (1/4)(√a)arccos(2x+1) ](x=-a/(1+a),0)
= (2a+3)(a^2)/{2(1+a)^2} -(1-a)a/{2(1+a)^2} -(1/4)arccos((1-a)/(1+a))
= (2a^2 +4a-1)a/{2(1+a)^2} - (1/2)arctan(√a),
S_3(a) = ∫[-a,0] x^2 dx = [ (1/3)x^3 ](x=-a, 0) = (1/3)a^3,