This is rather basic, and may be a misconception of the notation, however, I can't make the following sum up:(adsbygoogle = window.adsbygoogle || []).push({});

The following is given:

x_n(t) = 1 -nt , (if 0 <= t <= 1/n) and 0, (if 1/n < t <= 1)

However, this part I can't grasp this part in the book:

\begin{equation}

||x_n||^2 = \int_0^1 |x_n(t)|^2 dt = \frac{1}{3n}

\end{equation}

I tried it, and got a different answer, where i integrated ##|x_n(t)|^2=(1-nt)^2 = 1-2nt-n^2t^2##:

\begin{equation}

||x_n||^2 = \int_0^1 1-2nt-n^2t^2 dt = t - nt^2 -n^2t^2/3 = 1 - n - n^2/3

\end{equation}

The right answer is however given in the first integral. What did I do wrong here?

Thanks!

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# B How to interpret the integral of the absolute value?

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