integral from 0 to pi/3 of (9x-2)cos(3x)

Lösung

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

- 2

Schritte zur Lösung

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

Multipliziere aus

(9 x - 2) cos (3 x) : 9 x cos (3 x) - 2 cos (3 x)

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

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

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

= - 2 - 0

Vereinfache

= - 2

\int_{- 1}^{0} \frac{e ^{\frac{1}{θ}}}{θ ^{3}} d θ

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