integral from 1 to 2 of 2/((2x-5)^3)

Lösung

\int_{1}^{2} \frac{2}{( 2 x - 5 ) ^{3}} d x

- \frac{4}{9}

Dezimale

- 0.44444 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{2}{( 2 x - 5 ) ^{3}} d x

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{2} \frac{1}{( 2 x - 5 ) ^{3}} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

= 2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{- 3}^{- 1}

Vereinfache

2 \cdot \frac{1}{2} [- \frac{1}{2 u ^{2}}]_{- 3}^{- 1} : [- \frac{1}{2 u ^{2}}]_{- 3}^{- 1}

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

Berechne die Grenzen:

- \frac{4}{9}

= - \frac{4}{9}

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