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Beliebt Rechnen >

integral from 1 to 7 of 1/(9+(x+2)^2)

Lösung

\int_{1}^{7} \frac{1}{9 + ( x + 2 ) ^{2}} d x

Lösung

\frac{1}{3} (arctan (3) - \frac{π}{4})

+1

Dezimale

0.15454 \dots

Schritte zur Lösung

\int_{1}^{7} \frac{1}{9 + ( x + 2 ) ^{2}} d x

Wende U-Substitution an

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

Wende integrale Substitution an

= \int_{1}^{3} \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_{1}^{3} \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)]_{1}^{3}

Berechne die Grenzen:

arctan (3) - \frac{π}{4}

= \frac{1}{3} (arctan (3) - \frac{π}{4})

Graph

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