integral from-1 to 3 of x/(10-x^2)

Lösung

\int_{- 1}^{3} \frac{x}{10 - x ^{2}} d x

ln (3)

Dezimale

1.09861 \dots

Schritte zur Lösung

\int_{- 1}^{3} \frac{x}{10 - x ^{2}} d x

Wende U-Substitution an

= \int_{9}^{1} - \frac{1}{2 u} d u

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

= - \int_{1}^{9} - \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_{1}^{9} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{2} [ln ∣ u ∣]_{1}^{9})

Vereinfache

= \frac{1}{2} [ln ∣ u ∣]_{1}^{9}

Berechne die Grenzen:

2 ln (3)

= \frac{1}{2} \cdot 2 ln (3)

Vereinfache

= ln (3)

\int_{1}^{4} \frac{8 ( ln ( x ) ) ^{3}}{x} d x

\int_{\frac{1}{2}}^{2} ∣ ln (x) ∣ d x

\int_{\frac{1}{2}}^{1} (x^{- 3} - 11) d x

\int_{1}^{4} x + 1 d x

\int_{x}^{2 - x} 6 x^{2} y d y