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

Lösung

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

\frac{9 π}{4}

Dezimale

7.06858 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

\int \frac{9}{1 + x ^{2}} d x = 9 arctan (x) + C

Berechne die Grenzen:

\int_{1}^{\infty} \frac{9}{1 + x ^{2}} d x = 9 \cdot \frac{π}{2} - 9 \cdot \frac{π}{4}

= 9 \cdot \frac{π}{2} - 9 \cdot \frac{π}{4}

Vereinfache

= \frac{9 π}{4}

\int_{0}^{2 π} 8 d t

\int_{1}^{4} x x - 1 d x

\int_{0}^{x} 1 - t^{2} d t

\int_{0}^{2} 2 x + x^{2} - x^{3} d x

\int_{0}^{5} ∣ 1 - x ∣ d x