ZornsLemming
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 Jun7 awarded Supporter Jun6 awarded Scholar Jun6 accepted Integral inequality using positive and negative parts Jun6 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! Jun6 awarded Editor Jun6 comment Integral inequality using positive and negative parts I messed up h and f....ty, I corrected it. Jun6 revised Integral inequality using positive and negative parts corrected f and h Jun6 awarded Student Jun6 asked Integral inequality using positive and negative parts