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Math Help - integration

  1. #1
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    integration

    if equations 2x-y+z=0 ,x-2y+z=0 and tx-y+2z=0 have non trivial solutions and f(x)be continuous functions such that f(5+x)+f(x)=2 then integrate f(x) dx (limit 0 to -2t)
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Here are some hints to get you started.

    First find the determinant of this matrix and set it equal to zero and solve for t

    \begin{vmatrix}2 & -1 & 1 \\ 1 & -2 & 1 \\ t & -1 & 2 \end{vmatrix}=0

    For the 2nd part use the linearlity of the integral to break it up into two parts

    \displaystyle \int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}  f(x)dx

    Then make a u-substitution.

    Good luck and post your workings if you get stuck.
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