integral from-1 to 1 of (15)/((x+2)^2)

Lösung

\int_{- 1}^{1} \frac{15}{( x + 2 ) ^{2}} d x

10

Schritte zur Lösung

\int_{- 1}^{1} \frac{15}{( x + 2 ) ^{2}} d x

Entferne die Konstante:

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

= 15 \cdot \int_{- 1}^{1} \frac{1}{( x + 2 ) ^{2}} d x

Wende U-Substitution an

= 15 \cdot \int_{1}^{3} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 15 [- \frac{1}{u}]_{1}^{3}

Berechne die Grenzen:

\frac{2}{3}

= 15 \cdot \frac{2}{3}

Vereinfache

= 10

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