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Beliebt Rechnen >

integral from 4 to 10 of 1/(36+(x-4)^2)

Lösung

\int_{4}^{10} \frac{1}{36 + ( x - 4 ) ^{2}} d x

Lösung

\frac{π}{24}

+1

Dezimale

0.13089 \dots

Schritte zur Lösung

\int_{4}^{10} \frac{1}{36 + ( x - 4 ) ^{2}} d x

Wende U-Substitution an

= \int_{0}^{6} \frac{1}{36 + u ^{2}} d u

Wende integrale Substitution an

= \int_{0}^{1} \frac{1}{6 ( v ^{2} + 1 )} d v

Entferne die Konstante:

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

= \frac{1}{6} \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}{6} [arctan (v)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{6} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{24}

Graph

Beliebte Beispiele

derivative of \sqrt[6]{x}-6e^x

\frac{d}{d x} (6 x - 6 e^{x})

derivative of sqrt(9+x)

\frac{d}{d x} (9 + x)

inverselaplace 1/(9s^2+1)

in v erse l a pl a ce \frac{1}{9 s ^{2} + 1}

limit as t approaches 0 of e^{3t}

t \to 0 lim (e^{3 t})

tangent y=5-10x+x^3,\at x=-1

t an g e n t y = 5 - 10 x + x^{3}, at x = - 1