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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{6}

+1

Dezimale

0.16666 \dots

Schritte zur Lösung

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

Multipliziere aus

(x - 3) (4 - x) : 7 x - x^{2} - 12

= \int_{3}^{4} 7 x - x^{2} - 12 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_{3}^{4} 7 x d x - \int_{3}^{4} x^{2} d x - \int_{3}^{4} 12 d x

\int_{3}^{4} 7 x d x = \frac{49}{2}

\int_{3}^{4} x^{2} d x = \frac{37}{3}

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

= \frac{49}{2} - \frac{37}{3} - 12

Vereinfache

\frac{49}{2} - \frac{37}{3} - 12 : \frac{1}{6}

= \frac{1}{6}

Graph

Beliebte Beispiele

integral from 0 to pi of sqrt(2-2cos(t))

\int_{0}^{π} 2 - 2 cos (t) d t

integral from 0 to 2 of x/(1+10x^2)

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

integral from 1 to 8 of (1/x)

\int_{1}^{8} (\frac{1}{x}) d x

integral from 0 to 2 of 4-x

\int_{0}^{2} 4 - x d x

integral from-3 to 1 of 8

\int_{- 3}^{1} 8 d x