integral from 0 to a of 1/(sqrt(a-x))

Lösung

\int_{0}^{a} \frac{1}{a - x} d x

2 a

Schritte zur Lösung

\int_{0}^{a} \frac{1}{a - x} d x

Wende U-Substitution an

= \int_{a}^{0} - \frac{1}{u} d u

Entferne die Konstante:

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

= - \int_{a}^{0} \frac{1}{u} d u

Wende die Potenzregel an

= - [2 u^{\frac{1}{2}}]_{a}^{0}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= - [2 u]_{a}^{0}

Berechne die Grenzen:

- 2 a

= - (- 2 a)

Vereinfache

= 2 a

\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{1}{2} cos (x) d x

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

\int_{0}^{4} \frac{1}{e ^{x} + 1} d x

\int_{0}^{1} \frac{y ^{2}}{2} d y

\int_{2}^{3} \frac{1}{x ^{2} - 6 x + 10} d x