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 Feb 6 accepted Notational problem Feb 6 comment Notational problem Okay. Thanks very much. Feb 6 comment Notational problem One more thing... For the last term I have $j$ going from 4 to 3$. Isn't that a problem? Feb 6 comment Notational problem so what if I have instead$(c-a_2)(c-a_3)b_1 + (c-a_3)b_2 + b_3$? Would that be $$\sum\limits_{i=1}^3 \left( b_i \prod\limits_{j=i +1}^3 (c-a_j)\right)?$$ Feb 6 comment Notational problem Thanks JMoravitz. That's exactly what I was after. Feb 6 comment Notational problem @JMoravitz Thanks for your helpful comment. Feb 6 revised Notational problem added 6 characters in body Feb 6 comment Notational problem Can the person who down voted please explain why? Down voting without explaining doesn't help me improving the question if something is wrong it it. thanks. Feb 6 asked Notational problem Nov 7 awarded Yearling Oct 21 comment Triangle Inequality for norm integral$\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$. Thanks for not dismissing my comments. I appreciate you taking the trouble to edit the solution. You've been immense! +1 Oct 19 comment Triangle Inequality for norm integral$\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$. This is what I get. $$\left(\sqrt{\int_a^b(|f|+|f'|)^2dx}+\sqrt{\int_a^b(|g|+|g'|)^2dx}\right)^2 = \\ \int_a^b (|f|+|f'|)^2 dx + 2 \sqrt{\int_a^b (|f|+|f'|)^2 dx \int_a^b(|g|+|g'|)^2 dx} +\int_a^b (|g|+|g'|)^2 dx$$ Oct 19 comment Triangle Inequality for norm integral$\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$. I understand almost everything. it is the last two lines that are giving me problems. I don't see why\ $$\int_a^b(|f|^2+|f'|^2)dx+2\sqrt{\int_a^b(|f|+|f'|)^2dx\int_a^b(|g|+|g'|)^2dx}+‌​\int_a^b (|g|^2+|g'|^2)dx =\left(\sqrt{\int_a^b(|f|+|f'|)^2dx}+\sqrt{\int_a^b(|g|+|g'|)^2dx}\right)^2 =\left(||f||_1+||g||_1\right)^2$$ Oct 19 comment Triangle Inequality for norm integral$\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$. So what is it that am I not getting. Oct 19 comment Triangle Inequality for norm integral$\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$. Are there some hidden steps in your solution? I can't justify the going from the second to last line. Expanding the last but one line doesn't give the third line from the bottom. Also I thought$\|f\|_1 = \sqrt {\int_a^b( |f|^2 + |f'|^2)dx} $but it seems you are saying$\|f\|_1 = \sqrt {\int_a^b (|f|+|f'|)^2 dx}\$. Am I missing something? Oct 18 comment Establishing Triangle Inequality of a particular norm does this help in finishing the problem? Oct 18 comment Establishing Triangle Inequality of a particular norm @LutzL Yes. I know that, but how do I apply that. Oct 18 revised Establishing Triangle Inequality of a particular norm added 364 characters in body Oct 18 asked Establishing Triangle Inequality of a particular norm Oct 14 revised Property of an integral that vanishes added 17 characters in body