integral from 4 to 5 of x/(4-x^2)

Lösung

\int_{4}^{5} \frac{x}{4 - x ^{2}} d x

\frac{1}{2} ln (\frac{4}{7})

Dezimale

- 0.27980 \dots

Schritte zur Lösung

\int_{4}^{5} \frac{x}{4 - x ^{2}} d x

Wende U-Substitution an

= \int_{- 12}^{- 21} - \frac{1}{2 u} d u

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

= - \int_{- 21}^{- 12} - \frac{1}{2 u} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{- 21}^{- 12} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{2} [ln ∣ u ∣]_{- 21}^{- 12})

Vereinfache

= \frac{1}{2} [ln ∣ u ∣]_{- 21}^{- 12}

Berechne die Grenzen:

ln (12) - ln (21)

= \frac{1}{2} (ln (12) - ln (21))

Vereinfache

= \frac{1}{2} ln (\frac{4}{7})

\int_{0}^{1} \frac{9 x}{( 2 x + 1 ) ^{3}} d x

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

\int_{1}^{2} \frac{sin ( ln ( x ) )}{x} d x

\int_{0}^{4} \frac{x}{x ^{2} + 4} d x

\int_{x^{2}}^{4} y cos (y) d y