de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 3 of 1/(9+x^2)

Lösung

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

Lösung

\frac{π}{12}

+1

Dezimale

0.26179 \dots

Schritte zur Lösung

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

Wende integrale Substitution an

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

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}{u ^{2} + 1} d u

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

\frac{π}{4}

= \frac{1}{3} \cdot \frac{π}{4}

Vereinfache

= \frac{π}{12}

Graph

Beliebte Beispiele

tangent x^2-tan(x)

t an g e n t x^{2} - tan (x)

implicit (dy)/(dx),x^2-y^2=64

im pl i c i t \frac{d y}{d x}, x^{2} - y^{2} = 64

derivative of sec(pi/4)

\frac{d}{d x} (sec (\frac{π}{4}))

derivative cos((x+1)/(x-1))

d er i v a t i v e cos (\frac{x + 1}{x - 1})

derivative F(x)= 3/(1+x^2)

d er i v a t i v e F (x) = \frac{3}{1 + x ^{2}}