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awarded  Supporter
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awarded  Scholar
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accepted Integral inequality using positive and negative parts
Jun
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comment Integral inequality using positive and negative parts
Thanks a lot! This seems to work fine. So the idea was really to consider the two cases \int_{k\pi}^{(k+1)\pi}g(x)dx >= 0 and <0, instead of using the triangle inequality for the integral. But I don't think you need the "reverse" inequality, because in the case where \int_{k\pi}^{(k+1)\pi}g(x)dx < 0, you will get -\int_{k\pi}^{(k+1)\pi}g(x)dx \leq \frac{1}{k(k+1)\pi}\int_{0}^{\pi}f^+(x)dx. I would upvote your answer, but I havve not enough reputation. I will do it when I earned some more. Thank you!
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awarded  Editor
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comment Integral inequality using positive and negative parts
I messed up h and f....ty, I corrected it.
Jun
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revised Integral inequality using positive and negative parts
corrected f and h
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awarded  Student
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asked Integral inequality using positive and negative parts