integral from 0 to pi/2 of xcos(7x)

Lösung

\int_{0}^{\frac{π}{2}} x cos (7 x) d x

\frac{- 7 π - 2}{98}

Dezimale

- 0.24480 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} x cos (7 x) d x

Wende U-Substitution an

= \int_{0}^{\frac{7 π}{2}} \frac{u cos ( u )}{49} d u

Entferne die Konstante:

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

= \frac{1}{49} \cdot \int_{0}^{\frac{7 π}{2}} u cos (u) d u

Wende die partielle Integration an

= \frac{1}{49} [u sin (u) - \int sin (u) d u]_{0}^{\frac{7 π}{2}}

\int sin (u) d u = - cos (u)

= \frac{1}{49} [u sin (u) - (- cos (u))]_{0}^{\frac{7 π}{2}}

Vereinfache

= \frac{1}{49} [u sin (u) + cos (u)]_{0}^{\frac{7 π}{2}}

Berechne die Grenzen:

- \frac{7 π}{2} - 1

= \frac{1}{49} (- \frac{7 π}{2} - 1)

Vereinfache

= \frac{- 7 π - 2}{98}

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