integral from 0 to a of xsin(x)

Lösung

\int_{0}^{a} x sin (x) d x

sin (a) - a cos (a)

Schritte zur Lösung

\int_{0}^{a} x sin (x) d x

Wende die partielle Integration an

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

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{0}^{a}

Vereinfache

= [- x cos (x) + sin (x)]_{0}^{a}

Berechne die Grenzen:

sin (a) - a cos (a)

= sin (a) - a cos (a)

\int_{0}^{4} (x^{2} + 3) d x

\int_{0}^{4} x^{2} 2 x + 1 d x

\int_{a}^{b} e^{- x^{2}} d x

\int_{0}^{π} a sin (n x) d x

\int_{0}^{2} (x)^{2} d x