integral from 0 to 0.5 of xcosh(x^2+1)

Lösung

\int_{0}^{0.5} x cosh (x^{2} + 1) d x

0.21335 \dots

Schritte zur Lösung

\int_{0}^{0.5} x cosh (x^{2} + 1) d x

Wende U-Substitution an

= \int_{1}^{1.25} \frac{cosh ( u )}{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_{1}^{1.25} cosh (u) d u

Nutze das gemeinsame Integral :

\int cosh (u) d u = sinh (u)

= \frac{1}{2} [sinh (u)]_{1}^{1.25}

Vereinfache

= 0.5 [sinh (u)]_{1}^{1.25}

Berechne die Grenzen:

0.42671 \dots

= 0.5 \cdot 0.42671 \dots

Vereinfache

= 0.21335 \dots

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