integral from 0 to 1 of x/((4-x^2)^2)

Lösung

\int_{0}^{1} \frac{x}{( 4 - x ^{2} ) ^{2}} d x

\frac{1}{24}

Dezimale

0.04166 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{( 4 - x ^{2} ) ^{2}} d x

Wende U-Substitution an

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{3}^{4} \frac{1}{u ^{2}} d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [- \frac{1}{u}]_{3}^{4})

Vereinfache

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

Berechne die Grenzen:

\frac{1}{12}

= \frac{1}{2} \cdot \frac{1}{12}

Vereinfache

= \frac{1}{24}

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