integral from 0 to pi of x^2cos(n)x

Lösung

\int_{0}^{π} x^{2} cos (n) x d x

cos (n) \frac{π ^{4}}{4}

Schritte zur Lösung

\int_{0}^{π} x^{2} cos (n) x d x

Entferne die Konstante:

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

= cos (n) \cdot \int_{0}^{π} x^{2} x d x

Vereinfache

x^{2} x : x^{3}

= cos (n) \cdot \int_{0}^{π} x^{3} d x

Wende die Potenzregel an

= cos (n) [\frac{x ^{4}}{4}]_{0}^{π}

Berechne die Grenzen:

\frac{π ^{4}}{4}

= cos (n) \frac{π ^{4}}{4}

\int_{0}^{5} (x^{2} - 5) d x

\int_{- \frac{π}{3}}^{\frac{2 π}{3}} 3 tan (x) d x

\int_{0}^{4} (4 - y) d y

\int_{0}^{\frac{π}{2}} cos^{2} (3 x) d x

\int_{0}^{3} \frac{1}{3 x - x ^{2}} d x