integral from 0 to pi/5 of sin(5x)

Lösung

\int_{0}^{\frac{π}{5}} sin (5 x) d x

\frac{2}{5}

Dezimale

0.4

Schritte zur Lösung

\int_{0}^{\frac{π}{5}} sin (5 x) d x

Wende U-Substitution an

= \int_{0}^{π} sin (u) \frac{1}{5} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{0}^{π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{5} [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= \frac{1}{5} \cdot 2

Vereinfache

= \frac{2}{5}

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

\int_{0}^{7} 2 x \cdot 3 x + 1 d x

\int_{0}^{3} x^{2} e^{- 3 x} d x

\int_{r}^{\infty} \frac{1}{r ^{2}} d r

\int_{1}^{5} ∣ x - 2 ∣ d x