x^2/a^2 + y^2/b^2 = 1
y = (b/a)√(a^2 - x^2)
面积 = 4∫(0→a) (b/a)√(a^2 - x^2) dx,令x = a*sinθ,dx = a*cosθ dθ
= (4b/a)∫(0→π/2) √(a^2 - a^2sin^2θ)*(a*cosθ dθ)
= (4b/a)∫(0→π/2) (a*cosθ)(a*cosθ) dθ
= (4ab)∫(0→π/2) cos^2θ dθ
= (2ab)∫(0→π/2) (1 + cos2θ) dθ
= (2ab)[θ + (1/2)sin2θ] |(0→π/2)
= (2ab)(π/2)
= πab椭圆用y用x表示怎么得的？我是b2x2＋a2y2=a2b2.y2=b2－b2x2/a2.开了根号以后和你的结果不一样呀怎会不一样？你是不会解这个根号吧？代入x = a*sinθ就好了