∫(0~√2)(√(2-x∧2))dx
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解决时间 2021-11-26 13:20
- 提问者网友:雾里闻花香
- 2021-11-26 01:32
∫(0~√2)(√(2-x∧2))dx
最佳答案
- 五星知识达人网友:酒者煙囻
- 2021-11-26 02:10
如图所示
令x=√2·sint,则dx=√2·costdt
∫(0→√2)√(2-x²)dx
=∫(0→π/2)√2·cost·√2·cost dt
=∫(0→π/2)2·cos²t dt
=∫(0→π/2)(1+cos2t) dt
=[t+1/2·sin2t]|(0→π/2)
=π/2
令x=√2·sint,则dx=√2·costdt
∫(0→√2)√(2-x²)dx
=∫(0→π/2)√2·cost·√2·cost dt
=∫(0→π/2)2·cos²t dt
=∫(0→π/2)(1+cos2t) dt
=[t+1/2·sin2t]|(0→π/2)
=π/2
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