integral from 0 to 1 of xcos(pix)

Lösung

\int_{0}^{1} x cos (π x) d x

- \frac{2}{π ^{2}}

Dezimale

- 0.20264 \dots

Schritte zur Lösung

\int_{0}^{1} x cos (π x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

- \frac{2}{π ^{2}}

= - \frac{2}{π ^{2}}

\int (1 + cos (x))^{2} sin (x) d x

l a pl a ce t r an s f or m t^{2} e^{- 2 t} sin (3 t + 30)

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

x \to \infty lim (3 x^{3} - 1000 x^{2})

\int \frac{1}{x ^{2} - 2 x - 3} d x