integral from 0 to 1 of (x+1)sin(npix)

Lösung

\int_{0}^{1} (x + 1) sin (nπ x) d x

- \frac{( - 1 ) ^{n}}{πn} + \frac{- ( - 1 ) ^{n} + 1}{πn}

Schritte zur Lösung

\int_{0}^{1} (x + 1) sin (nπ x) d x

Multipliziere aus

(x + 1) sin (nπ x) : x sin (πn x) + sin (πn x)

= \int_{0}^{1} x sin (πn x) + sin (πn x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x sin (πn x) d x + \int_{0}^{1} sin (πn x) d x

\int_{0}^{1} x sin (πn x) d x = - \frac{( - 1 ) ^{n}}{πn}

\int_{0}^{1} sin (πn x) d x = \frac{- ( - 1 ) ^{n} + 1}{πn}

= - \frac{( - 1 ) ^{n}}{πn} + \frac{- ( - 1 ) ^{n} + 1}{πn}

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