функция задана кусочно:
[m]\left\{\begin {matrix}2, x ∈ [-1;1)\\0, x ∈ [1;3)\end {matrix}\right.[/m]
T=4
[m] l=2[/m]
[m]a_{o}=\frac{1}{2} ∫_{-1} ^{1}2dx+\frac{1}{2} ∫_{1} ^{3}0dx=\frac{1}{2}(2x)|_{-1} ^{1}=(1-(-1))=2[/m]
[m]a_{n}=\frac{1}{2} ∫_{-1} ^{1}2 \cdot cos\frac{nπx}{2}dx+\frac{1}{2} ∫_{1} ^{3}0\cdot cos\frac{nπx}{2}dx=\frac{2}{πn} sin\frac{nπx}{2}|_{-1} ^{1}[/m]
[m]b_{n}=\frac{1}{2} ∫_{-1} ^{1}2 \cdot sin\frac{nπx}{2}dx+\frac{1}{2} ∫_{1} ^{3}0\cdot cos\frac{nπx}{2}dx=-\frac{2}{πn} cos\frac{nπx}{2}|^{1}_{-1}= [/m]