integral from-7 to 8 of 1/(sqrt(8-x))

Lösung

\int_{- 7}^{8} \frac{1}{8 - x} d x

215

Dezimale

7.74596 \dots

Schritte zur Lösung

\int_{- 7}^{8} \frac{1}{8 - x} d x

Wende U-Substitution an

= \int_{15}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{15} - \frac{1}{u} d u

Entferne die Konstante:

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

= - (- \int_{0}^{15} \frac{1}{u} d u)

Wende die Potenzregel an

= - (- [2 u^{\frac{1}{2}}]_{0}^{15})

Vereinfache

- (- [2 u^{\frac{1}{2}}]_{0}^{15}) : [2 u]_{0}^{15}

= [2 u]_{0}^{15}

Berechne die Grenzen:

215

= 215

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