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Beliebt Rechnen >

integral from 1 to 4 of 1/(9+(x-1)^2)

Lösung

\int_{1}^{4} \frac{1}{9 + ( x - 1 ) ^{2}} d x

Lösung

\frac{π}{12}

+1

Dezimale

0.26179 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{1}{9 + ( x - 1 ) ^{2}} d x

Wende U-Substitution an

= \int_{0}^{3} \frac{1}{9 + u ^{2}} d u

Wende integrale Substitution an

= \int_{0}^{1} \frac{1}{3 ( v ^{2} + 1 )} d v

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{1} \frac{1}{v ^{2} + 1} d v

Nutze das gemeinsame Integral :

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= \frac{1}{3} [arctan (v)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{3} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{12}

Graph

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