integral from 0 to x/2 of sqrt(sin(x))

Lösung

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

- 2 E (2 \cdot \frac{1}{2} ∣ (\frac{π}{2} - \frac{x}{2})) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

Schritte zur Lösung

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

Das ist ein nicht elementares Integral :

\int sin (x) d x = - 2 E (\frac{1}{2} (\frac{π}{2} - x) ∣ 2)

= [- 2 E (\frac{1}{2} (\frac{π}{2} - x) ∣ 2)]_{0}^{\frac{x}{2}}

Berechne die Grenzen:

- 2 E (2 \cdot \frac{1}{2} ∣ (\frac{π}{2} - \frac{x}{2})) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

= - 2 E (2 \cdot \frac{1}{2} ∣ (\frac{π}{2} - \frac{x}{2})) + 2 E (2 \cdot \frac{1}{2} (\frac{π}{2} - 0) ∣)

\int_{1}^{\infty} \frac{8}{x ^{5}} d x

\int_{- \frac{π}{9}}^{\frac{π}{9}} sec^{3} (3 x) d x

\int_{4}^{14} \frac{1}{x} d x

\int_{- 1}^{1} (8 x^{2} - 1)^{2} d x

\int_{- π}^{0} x - π d x