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Beliebt Rechnen >

integral from 1 to sqrt(3 of) 4/(x^2+1)

Lösung

\int_{1}^{3} \frac{4}{x ^{2} + 1} d x

Lösung

\frac{π}{3}

+1

Dezimale

1.04719 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{4}{x ^{2} + 1} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{3} \frac{1}{x ^{2} + 1} d x

Nutze das gemeinsame Integral :

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

= 4 [arctan (x)]_{1}^{3}

Berechne die Grenzen:

\frac{π}{12}

= 4 \cdot \frac{π}{12}

Vereinfache

= \frac{π}{3}

Graph

Beliebte Beispiele

integral from-2 to 2 of 4(4-x^2)

\int_{- 2}^{2} 4 (4 - x^{2}) d x

(d^2)/(dx^2)(x/(x^2-9))

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x ^{2} - 9})

integral of sec^2(7/3 x+4)

\int sec^{2} (\frac{7}{3} x + 4) d x

integral of (2x-e^x)

\int (2 x - e^{x}) d x

limit as x approaches 0 of (sin(10x))/(11x)

x \to 0 lim (\frac{sin ( 10 x )}{11 x})