integral from 0 to pi/2 of sinh(2x)

Lösung

\int_{0}^{\frac{π}{2}} sinh (2 x) d x

\frac{e ^{2 π} + 1 - 2 e ^{π}}{4 e ^{π}}

Dezimale

5.29597 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} sinh (2 x) d x

Wende U-Substitution an

= \int_{0}^{π} sinh (u) \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}^{π} sinh (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [cosh (u)]_{0}^{π}

Berechne die Grenzen:

\frac{e ^{2 π} + 1}{2 e ^{π}} - 1

= \frac{1}{2} (\frac{e ^{2 π} + 1}{2 e ^{π}} - 1)

Vereinfache

= \frac{e ^{2 π} + 1 - 2 e ^{π}}{4 e ^{π}}

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