integral from 0 to 2 of x^2cos((npix)/2)

Soluzione

\int_{0}^{2} x^{2} cos (\frac{nπ x}{2}) d x

\frac{16 ( - 1 ) ^{n}}{π ^{2} n ^{2}}

Fasi della soluzione

\int_{0}^{2} x^{2} cos (\frac{nπ x}{2}) d x

Applica l'Integrazione per Parti

= [\frac{2}{πn} x^{2} sin (\frac{πn x}{2}) - \int \frac{4}{πn} x sin (\frac{πn x}{2}) d x]_{0}^{2}

\int \frac{4}{πn} x sin (\frac{πn x}{2}) d x = \frac{16}{π ^{3} n ^{3}} (- \frac{πn}{2} x cos (\frac{πn x}{2}) + sin (\frac{πn x}{2}))

= [\frac{2}{πn} x^{2} sin (\frac{πn x}{2}) - \frac{16}{π ^{3} n ^{3}} (- \frac{πn}{2} x cos (\frac{πn x}{2}) + sin (\frac{πn x}{2}))]_{0}^{2}

Calcola i limiti:

\frac{16 ( - 1 ) ^{n}}{π ^{2} n ^{2}}

= \frac{16 ( - 1 ) ^{n}}{π ^{2} n ^{2}}

\int_{0}^{e + 1} \frac{x + 1}{x ^{2} - 1} d x

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