integral from 0 to pi of 1cos(n)x

Lösung

\int_{0}^{π} 1 cos (n) x d x

cos (n) \frac{π ^{2}}{2}

Schritte zur Lösung

\int_{0}^{π} 1 \cdot cos (n) x d x

Entferne die Konstante:

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

= 1 \cdot cos (n) \cdot \int_{0}^{π} x d x

Vereinfache

= cos (n) \cdot \int_{0}^{π} x d x

Wende die Potenzregel an

= cos (n) [\frac{x ^{2}}{2}]_{0}^{π}

Berechne die Grenzen:

\frac{π ^{2}}{2}

= cos (n) \frac{π ^{2}}{2}

\int_{0}^{2} x^{4} - 4 x^{2} d x

\int_{- 0.5}^{0.5} x^{2} d x

\int_{2}^{4} 2 x (4 + x^{2})^{3} d x

\int_{0}^{5} \frac{x}{a + b x ^{2}} d x

\int_{0}^{1} x^{9} (1 + x^{10})^{9} d x