integral from 1 to 5 of 1/((10-x)^2)

Lösung

\int_{1}^{5} \frac{1}{( 10 - x ) ^{2}} d x

\frac{4}{45}

Dezimale

0.08888 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{1}{( 10 - x ) ^{2}} d x

Wende U-Substitution an

= \int_{9}^{5} - \frac{1}{u ^{2}} d u

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

= - \int_{5}^{9} - \frac{1}{u ^{2}} d u

Entferne die Konstante:

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

= - (- \int_{5}^{9} \frac{1}{u ^{2}} d u)

Wende die Potenzregel an

= - (- [- \frac{1}{u}]_{5}^{9})

Vereinfache

= [- \frac{1}{u}]_{5}^{9}

Berechne die Grenzen:

\frac{4}{45}

= \frac{4}{45}

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