integral from 0 to sqrt(pi of)-xsin(x^2)

Lösung

\int_{0}^{π} - x sin (x^{2}) d x

- 1

Schritte zur Lösung

\int_{0}^{π} - x sin (x^{2}) d x

Entferne die Konstante:

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

= - \int_{0}^{π} x sin (x^{2}) d x

Wende U-Substitution an

= - \int_{0}^{π} \frac{sin ( 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_{0}^{π} sin (u) d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{2} [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= - \frac{1}{2} \cdot 2

Vereinfache

= - 1

\int_{9}^{15} x d x

\int_{2}^{4} k [1 - (x - 3)^{2}] d x

\int_{0}^{π} e^{x} cos (n x) d x

\int_{2}^{3} x - 1 d x

\int_{π}^{0} sin^{2} (x) d x