integral from 0 to 1 of 4/(pi(1+x^2))

Lösung

\int_{0}^{1} \frac{4}{π ( 1 + x ^{2} )} d x

1

Schritte zur Lösung

\int_{0}^{1} \frac{4}{π ( 1 + x ^{2} )} d x

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= \frac{4}{π} [arctan (x)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= \frac{4}{π} \cdot \frac{π}{4}

Vereinfache

= 1

\int_{\frac{- π}{2}}^{\frac{π}{2}} x cos (x) d x

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

\int_{0}^{3} 2 x (x - 7) d x

\int_{x}^{π} sin (y^{2}) d y

\int_{1}^{2} x ln (x - 1) d x