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

Lösung

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

- arctan (2) + 2

Dezimale

0.89285 \dots

Schritte zur Lösung

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

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

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

Wende die Summenregel an:

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

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

\int_{0}^{2} \frac{1}{x ^{2} + 1} d x = arctan (2)

\int_{0}^{2} 1 d x = 2

= - arctan (2) + 2

\int_{1}^{2} 1 + \frac{9 x}{4} d x

\int_{- 1}^{2} (y^{2} - y - 2) d y

\int_{0}^{\infty} \frac{5}{x ^{2} + 6} d x

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

\int_{0}^{4} x^{2} - 7 x + 12 d x