integral from 0 to 1 of xsin(npix)

Lösung

\int_{0}^{1} x sin (nπ x) d x

- \frac{( - 1 ) ^{n}}{πn}

Schritte zur Lösung

\int_{0}^{1} x sin (nπ x) d x

Wende die partielle Integration an

= [- \frac{1}{πn} x cos (πn x) - \int - \frac{1}{πn} cos (πn x) d x]_{0}^{1}

\int - \frac{1}{πn} cos (πn x) d x = - \frac{1}{π ^{2} n ^{2}} sin (πn x)

= [- \frac{1}{πn} x cos (πn x) - (- \frac{1}{π ^{2} n ^{2}} sin (πn x))]_{0}^{1}

Vereinfache

= [- \frac{1}{πn} x cos (πn x) + \frac{1}{π ^{2} n ^{2}} sin (πn x)]_{0}^{1}

Berechne die Grenzen:

- (- 1)^{n} \frac{1}{πn}

= - (- 1)^{n} \frac{1}{πn}

Vereinfache

= - \frac{( - 1 ) ^{n}}{πn}

\frac{\partial}{\partial y} (y^{4})

\frac{d}{d x} (sec (x) \cdot x^{5})

\frac{\partial}{\partial x} (x + 2 y + z)

\int \frac{12 x + 30}{x ^{2} + 2 x - 8} d x

x \to 1 lim (e^{x^{2} + 7 x - 8})