beloved_zhe
幼苗
共回答了18个问题采纳率:88.9% 举报
令x = √2siny.dx = √2cosy dy
∫ √(2 - x^2) dx
= ∫ √(2 - 2sin^2y)(√2cosy dy)
= 2∫ cos^2y dy
= ∫ (1 + cos2y) dy
= y + (1/2)sin2y + C
= y + siny√(1 - sin^2y) + C
= arcsin(x/√2) + (x/√2)√(1 - x^2/2) + C
= arcsin(x/√2) + (x/2)√(2 - x^2) + C
1年前
11