integral from 0 to 2 of ln(3-x)

Lösung

\int_{0}^{2} ln (3 - x) d x

3 ln (3) - 2

Dezimale

1.29583 \dots

Schritte zur Lösung

\int_{0}^{2} ln (3 - x) d x

Wende U-Substitution an

= \int_{3}^{1} - ln (u) d u

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

= - \int_{1}^{3} - ln (u) d u

Entferne die Konstante:

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

= - (- \int_{1}^{3} ln (u) d u)

Wende die partielle Integration an

= - (- [u ln (u) - \int 1 d u]_{1}^{3})

\int 1 d u = u

= - (- [u ln (u) - u]_{1}^{3})

Vereinfache

= [u ln (u) - u]_{1}^{3}

Berechne die Grenzen:

3 ln (3) - 2

= 3 ln (3) - 2

\int_{- 1}^{1} x arccos (x) d x

\int_{0}^{2} x^{2} - 40 d x

\int_{1}^{3} x^{2} - 3 x + 1 d x

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

\int_{0}^{\frac{π}{2}} 3 cos^{3} (x) d x