integral from 2 to 6 of (x^2+7x-5)(x-2)

Lösung

\int_{2}^{6} (x^{2} + 7 x - 5) (x - 2) d x

\frac{1208}{3}

Dezimale

402.66666 \dots

Schritte zur Lösung

\int_{2}^{6} (x^{2} + 7 x - 5) (x - 2) d x

Multipliziere aus

(x^{2} + 7 x - 5) (x - 2) : x^{3} + 5 x^{2} - 19 x + 10

= \int_{2}^{6} x^{3} + 5 x^{2} - 19 x + 10 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_{2}^{6} x^{3} d x + \int_{2}^{6} 5 x^{2} d x - \int_{2}^{6} 19 x d x + \int_{2}^{6} 10 d x

\int_{2}^{6} x^{3} d x = 320

\int_{2}^{6} 5 x^{2} d x = \frac{1040}{3}

\int_{2}^{6} 19 x d x = 304

\int_{2}^{6} 10 d x = 40

= 320 + \frac{1040}{3} - 304 + 40

Vereinfache

320 + \frac{1040}{3} - 304 + 40 : \frac{1208}{3}

= \frac{1208}{3}

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

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin^{2} (x) d x

\int_{1}^{5} \frac{2}{x ^{2}} d x

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

\int_{- 1}^{1} x (x^{2} + 4)^{3} d x