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Beliebt Rechnen >

integral from-a to a of |a+3t|

Lösung

\int_{- a}^{a} ∣ a + 3 t ∣ d t

Lösung

\frac{10 a ∣ a ∣}{3}

Schritte zur Lösung

\int_{- a}^{a} ∣ a + 3 t ∣ d t

Wende U-Substitution an

= \int_{- 2 a}^{4 a} ∣ u ∣ \frac{1}{3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{- 2 a}^{4 a} ∣ u ∣ d u

Nutze das gemeinsame Integral :

\int ∣ u ∣ d u = \frac{u ∣ u ∣}{2}

= \frac{1}{3} [\frac{u ∣ u ∣}{2}]_{- 2 a}^{4 a}

Berechne die Grenzen:

10 a ∣ a ∣

= \frac{1}{3} \cdot 10 a ∣ a ∣

Vereinfache

= \frac{10 a ∣ a ∣}{3}

Beliebte Beispiele

integral from 0 to 2 of r

\int_{0}^{2} r d r

integral from 0 to 3 of pi(x^2)^2

\int_{0}^{3} π (x^{2})^{2} d x

integral from 3 to 7 of (1+2x)

\int_{3}^{7} (1 + 2 x) d x

integral from 0 to 2 of (x+3)

\int_{0}^{2} (x + 3) d x

integral from-2 to 3 of x+3

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