∫(0→√2a) x/√(3a² - x²) dx。令x = √3a * sinz，dx = √3a * cosz dz
x = 0 → z = 0
x = √2a → z = arcsin√(2/3)
= ∫(0→arcsin√(2/3)) (√3a * sinz)/|√3a * cosz| * (√3a * cosz dz)
= ∫(0→arcsin√(2/3)) √3a * sinz dz
= - √3a * cosz dz |(0→arcsin√(2/3))
= - √3a * cos(arcsin√(2/3)) + √3a * 1
= - √3a * 1/√3 + √3a
= (√3 - 1)a，(a > 0)
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024