integral from 0 to pi of (2x-1)cos(3x)

Lösung

\int_{0}^{π} (2 x - 1) cos (3 x) d x

- \frac{4}{9}

Dezimale

- 0.44444 \dots

Schritte zur Lösung

\int_{0}^{π} (2 x - 1) cos (3 x) d x

Multipliziere aus

(2 x - 1) cos (3 x) : 2 x cos (3 x) - cos (3 x)

= \int_{0}^{π} 2 x cos (3 x) - cos (3 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}^{π} 2 x cos (3 x) d x - \int_{0}^{π} cos (3 x) d x

\int_{0}^{π} 2 x cos (3 x) d x = - \frac{4}{9}

\int_{0}^{π} cos (3 x) d x = 0

= - \frac{4}{9} - 0

Vereinfache

= - \frac{4}{9}

\int_{- π}^{π} 2 sin (x) d x

\int_{0}^{y} e^{t^{4}} d t

\int_{0}^{1} 6 x^{2} (1 - x) d x

\int_{- 2}^{2} sin (x) d x

\int_{1}^{e^{x}} 8 ln (t) d t