integral from 0 to 1 of x/((x^2-4)^3)

Lösung

\int_{0}^{1} \frac{x}{( x ^{2} - 4 ) ^{3}} d x

- \frac{7}{576}

Dezimale

- 0.01215 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{x}{( x ^{2} - 4 ) ^{3}} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

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

Berechne die Grenzen:

- \frac{7}{288}

= \frac{1}{2} (- \frac{7}{288})

Vereinfache

= - \frac{7}{576}

\int_{- 7}^{28} x 3 1 - x d x

\int_{1}^{2} - \frac{1}{z} d z

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

\int_{0}^{1} x^{3} - 4 x d x

\int_{0}^{5} (x - 2)^{25} d x