integral from 2 to 4 of 1/(tsqrt(t^2-4))

Lösung

\int_{2}^{4} \frac{1}{t t ^{2} - 4} d t

\frac{π}{6}

Dezimale

0.52359 \dots

Schritte zur Lösung

\int_{2}^{4} \frac{1}{t t ^{2} - 4} d t

Trigonometrische Substitution anwenden

= \int_{0}^{\frac{π}{3}} \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{3}} 1 d u

Integral einer Konstanten :

\int a d x = a x

= \frac{1}{2} [1 \cdot u]_{0}^{\frac{π}{3}}

Vereinfache

= \frac{1}{2} [u]_{0}^{\frac{π}{3}}

Berechne die Grenzen:

\frac{π}{3}

= \frac{1}{2} \cdot \frac{π}{3}

Vereinfache

= \frac{π}{6}

\int_{0}^{6} x e^{x^{2}} d x

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