设f为[0,+∞)上连续的严格递增函数,f(0)=0证明:ab≤∫0到a f(x)dx+∫0到b f-1(y)dy (-1代表负一次方)当且仅当b=f(a)时,等号成立(a,b≥0)
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![设f为[0,+∞)上连续的严格递增函数,f(0)=0证明:ab≤∫0到a f(x)dx+∫0到b f-1(y)dy (-1代表负一次方)当且仅当b=f(a)时,等号成立(a,b≥0)](/uploads/image/z/3817232-8-2.jpg?t=%E8%AE%BEf%E4%B8%BA%5B0%2C%2B%E2%88%9E%EF%BC%89%E4%B8%8A%E8%BF%9E%E7%BB%AD%E7%9A%84%E4%B8%A5%E6%A0%BC%E9%80%92%E5%A2%9E%E5%87%BD%E6%95%B0%2Cf%280%29%3D0%E8%AF%81%E6%98%8E%EF%BC%9Aab%E2%89%A4%E2%88%AB0%E5%88%B0a+f%28x%29dx%2B%E2%88%AB0%E5%88%B0b+f-1%28y%29dy+%28-1%E4%BB%A3%E8%A1%A8%E8%B4%9F%E4%B8%80%E6%AC%A1%E6%96%B9%EF%BC%89%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93b%3Df%28a%29%E6%97%B6%2C%E7%AD%89%E5%8F%B7%E6%88%90%E7%AB%8B%EF%BC%88a%2Cb%E2%89%A50%EF%BC%89)
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