integral from 0 to pi of-xcos(x)

Lösung

\int_{0}^{π} - x cos (x) d x

2

Schritte zur Lösung

\int_{0}^{π} - x cos (x) d x

Entferne die Konstante:

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

= - \int_{0}^{π} x cos (x) d x

Wende die partielle Integration an

= - [x sin (x) - \int sin (x) d x]_{0}^{π}

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

= - [x sin (x) - (- cos (x))]_{0}^{π}

Vereinfache

= - [x sin (x) + cos (x)]_{0}^{π}

Berechne die Grenzen:

- 2

= - (- 2)

Vereinfache

= 2

\int_{- 2}^{1} (2 t^{2} - 1)^{2} d t

\int_{1}^{x} 1 + t d t

\int_{0}^{1} (x^{\frac{1}{2}} - x^{2}) d x

\int_{0}^{5} 7 d x

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