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 2 of (x^2)/(x^2+4)

Lösung

\int_{0}^{2} \frac{x ^{2}}{x ^{2} + 4} d x

Lösung

2 (- \frac{π}{4} + 1)

+1

Dezimale

0.42920 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{x ^{2}}{x ^{2} + 4} d x

\frac{x ^{2}}{x ^{2} + 4} = - \frac{4}{x ^{2} + 4} + 1

= \int_{0}^{2} - \frac{4}{x ^{2} + 4} + 1 d x

Wende integrale Substitution an

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

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} - \frac{1}{u ^{2} + 1} + 1 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{1} \frac{1}{u ^{2} + 1} d u = \frac{π}{4}

\int_{0}^{1} 1 d u = 1

= 2 (- \frac{π}{4} + 1)

Graph

Beliebte Beispiele

integral of (2-3x)^2

ydx=(ye^{y-2x})dy

derivative f(x)=sqrt(6-7x)

limit as x approaches infinity of (5x+6x^2)/(3x-8)

laplacetransform 1/2