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

Lösung

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

\frac{3}{22}

Dezimale

0.13636 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{11} \frac{1}{3 u ^{2}} 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}^{11} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= \frac{1}{3} [- \frac{1}{u}]_{2}^{11}

Berechne die Grenzen:

\frac{9}{22}

= \frac{1}{3} \cdot \frac{9}{22}

Vereinfache

= \frac{3}{22}

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