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 Sep 24 awarded Autobiographer Aug 1 comment How find the maximum of the value $x^2_{1}+x^2_{2}+\cdots+x^2_{2014}$ Sorry,. You have edited it. Originally it's -11k+ 5(2014-k) + x_2014 =0. I'm reading the post on my phone, and I can't see the updates immediately. Aug 1 awarded Commentator Aug 1 comment How find the maximum of the value $x^2_{1}+x^2_{2}+\cdots+x^2_{2014}$ There are (2013-k) 5 (ideally, there should be (2014-k) 5, but this condition won't lead to an integer solution), so your equation should be corrected and so should the maximum. Nov 5 awarded Yearling Feb 13 comment Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$? @Peter Because the op guessed $\int_a^b f(x) dx = (f(b)-f(a))b - \int_{f(a)}^{f(b)}f^{-1}(x)dx$ , I just wan to show him his guess is close to the fact. Feb 7 awarded Supporter Feb 7 comment Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$? Furthermore, we can get $\int_a^b f(x)dx = x f(x)|_a^b - \int_a^b x f'(x)dx = x f(x)|_a^b - \int_a^b f^{-1}(f(x)) f'(x)dx=x f(x)|_a^b - \int_{f(a)}^{f(b)} f^{-1}(u) du(u=f(x))=x f(x)|_a^b - \int_{f(a)}^{f(b)} f^{-1}(x) dx$, so your guess is close to the fact that $\int_a^b f(x) dx = bf(b)-af(a) - \int_{f(a)}^{f(b)}f^{-1}(x)dx$ Dec 8 revised Why is arctan of $-\frac{\sqrt{3}}{3} = -\frac{1}{6}\pi$? In my opinion,a open interval should be noted as" (a, b)", instead of " ]a,b[". A typo? Dec 8 suggested approved edit on Why is arctan of $-\frac{\sqrt{3}}{3} = -\frac{1}{6}\pi$? Dec 6 comment Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ absolutely I am not offended.actually, thanks for your comment! I have much to learn here and I love math. Dec 5 awarded Editor Dec 5 revised Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ added 376 characters in body Dec 5 comment Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ @DylanMoreland: Sorry, I just typed my comment on my phone. You know, it's slower to type than on a computer. And I finished my comment without care. That's why I showed such a strange comment... Dec 5 comment Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ of course,two points can't tell me that. However, I think a function in the form $f(x)=x^n,n\in \mathbb N$ is elementary and it's monotonicity in $[0,\infty)$ is obvious. I am not familiar with Math jargons in English, but I can show it. Dec 5 comment Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ of course,two points can't tell me that. However, I think a function in the form $f(x)=x^n,n\in \mathbb N$ is an Dec 5 answered Prove that the equation $x^{10000} + x^{100} - 1 = 0$ has a solution with $0 < x < 1$ Dec 3 answered How to find center of an arc given start point, end point, radius, and arc direction? Dec 1 answered Any idea how to solve this equation? Nov 28 answered Finding all functions $f$ satisfying $f'(t)=f(t)+\int_a^bf(t)dt$