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Beliebt Rechnen >

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

Lösung

\int_{- 1}^{1} \frac{2}{1 + x ^{2}} d x

Lösung

π

+1

Dezimale

3.14159 \dots

Schritte zur Lösung

\int_{- 1}^{1} \frac{2}{1 + x ^{2}} d x

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= 2 [arctan (x)]_{- 1}^{1}

Berechne die Grenzen:

\frac{π}{2}

= 2 \cdot \frac{π}{2}

Vereinfache

= π

Graph

Beliebte Beispiele

(dx)/(dt)=12-(27x)/(900-15t)

\frac{d x}{d t} = 12 - \frac{27 x}{900 - 15 t}

integral of (sin(x))/(1+sin^2(x))

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

(\partial)/(\partial θ)(sin(θ)cos(φ))

\frac{\partial}{\partial θ} (sin (θ) cos (φ))

integral of 4x-6xy^2-2

\int 4 x - 6 x y^{2} - 2 d x

t^2y^{''}+19ty^'+130y=0

t^{2} y^{^{''}} + 19 t y^{^{'}} + 130 y = 0