integral from 0 to 4 of (x-3)(x-1)

Lösung

\int_{0}^{4} (x - 3) (x - 1) d x

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{0}^{4} (x - 3) (x - 1) d x

Multipliziere aus

(x - 3) (x - 1) : x^{2} - 4 x + 3

= \int_{0}^{4} x^{2} - 4 x + 3 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}^{4} x^{2} d x - \int_{0}^{4} 4 x d x + \int_{0}^{4} 3 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 4 x d x = 32

\int_{0}^{4} 3 d x = 12

= \frac{64}{3} - 32 + 12

Vereinfache

\frac{64}{3} - 32 + 12 : \frac{4}{3}

= \frac{4}{3}

\int_{- 1}^{3} \frac{1}{x ^{3}} d x

\int_{0}^{1} \frac{1}{y} d y

\int_{- 1}^{5} ∣ x ∣ d x

\int_{0}^{1} \frac{2}{5} (2 x + 3 y) d y

\int_{- 2}^{3} x^{2} d x