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Beliebt Rechnen >

integral of 2x^2cos((npix)/2)

Lösung

\int 2 x^{2} cos (\frac{nπ x}{2}) d x

Lösung

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}))) + C

Schritte zur Lösung

\int 2 x^{2} cos (\frac{nπ x}{2}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x^{2} cos (\frac{nπ x}{2}) d x

Wende die partielle Integration an

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

\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}))

= 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})))

Füge eine Konstante zur Lösung hinzu

= 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}))) + C

Graph

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