展开 xsin((pinx)/L)(L-x)

解答

展开

x sin (\frac{πn x}{L}) (L - x)

xL sin (\frac{πn x}{L}) - x^{2} sin (\frac{πn x}{L})

求解步骤

x sin (\frac{πn x}{L}) (L - x)

使用分配律:

a (b - c) = ab - a c

a = x sin (\frac{πn x}{L}), b = L, c = x

= x sin (\frac{πn x}{L}) L - x sin (\frac{πn x}{L}) x

= xL sin (\frac{πn x}{L}) - xx sin (\frac{πn x}{L})

xx sin (\frac{πn x}{L}) = x^{2} sin (\frac{πn x}{L})

= xL sin (\frac{πn x}{L}) - x^{2} sin (\frac{πn x}{L})

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