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Math Help - Integral over a subdivided integral

  1. #1
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    Integral over a subdivided integral

    Divide [0,1] into N subintervals (x_k,x_{k+1}), k=0,...,N-1 using x_k=kh,k=0,...,N, h=\frac{1}{N}, N\geq 2.

    Let \phi_k(x)=\left(1-\left| \frac{x-x_k}{h}\right|\right)_{+}, k=1,...,N-1 and let p,q be constant functions over [0,1].

    I'm trying to find the piecewise solution to the integral \int_0^1\left[ p \phi_j' \phi_i' + q \phi_j \phi_i\right]\ dx. The solution is given in my notes without any explanation so I must be missing something because I'm not sure how to do it.

    If someone can show me how to find e.g. \int_0^1 \phi_j \phi_i \ dx then I should be able to do the rest. I can see that the solution will only be non-zero in the region |i-j|=1 and i=j but I'm struggling from here.
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  2. #2
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    Can anyone help?
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