integral from 1 to pi of cos(3t)+8t

Lösung

\int_{1}^{π} cos (3 t) + 8 t d t

- \frac{1}{3} sin (3) + 4 (π^{2} - 1)

Dezimale

35.43137 \dots

Schritte zur Lösung

\int_{1}^{π} cos (3 t) + 8 t d t

Wende die Summenregel an:

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

= \int_{1}^{π} cos (3 t) d t + \int_{1}^{π} 8 t d t

\int_{1}^{π} cos (3 t) d t = - \frac{1}{3} sin (3)

\int_{1}^{π} 8 t d t = 4 (π^{2} - 1)

= - \frac{1}{3} sin (3) + 4 (π^{2} - 1)