9. (a) State and prove orthogonal p...
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9. (a) State and prove orthogonal properties of Legendre polynomials.

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Maths
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[ begin{array}{l} int_{-1}^{1} f_{n}(x) P_{n}(x) d x=2(-1)^{n} frac{a_{n}}{2^{n}} int_{0}^{1}left(x^{2}-1right)^{n} d x=2(-1)^{n} frac{a_{n}}{2^{n}} cdot I_{n} end{array} ] ( ldots ldots . .(6) ) ldon't understand as in shouldnt it be like this, [ begin{array}{c} int_{-1}^{1} f_{n}(x) P_{n}(x) d x=(-1)^{n} frac{a_{n}}{2^{n}} int_{-1}^{1}left(x^{2}-1right)^{n} d x=0 end{array} ] as they should cancel out even if the integral is non-zero.
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