integral from 0 to 1 of (x/(1+x^4))

Lösung

\int_{0}^{1} (\frac{x}{1 + x ^{4}}) d x

\frac{π}{8}

Dezimale

0.39269 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

\int \frac{x}{1 + x ^{4}} d x = \frac{1}{2} arctan (x^{2}) + C

Berechne die Grenzen:

\int_{0}^{1} (\frac{x}{1 + x ^{4}}) d x = \frac{π}{8} - 0

= \frac{π}{8} - 0

Vereinfache

= \frac{π}{8}

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

\int_{1}^{3} \frac{x + 3}{x ^{2} + 6 x} d x

\int_{4}^{\infty} \frac{6}{x ^{4}} d x

\int_{0}^{1} (\frac{y}{e ^{2 y}}) d y

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