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Beliebt Rechnen >

integral from 0 to pi/4 of sin(sqrt(x))

Lösung

\int_{0}^{\frac{π}{4}} sin (x) d x

Lösung

2 sin (\frac{π}{2}) - π cos (\frac{π}{2})

+1

Dezimale

0.42859 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} sin (x) d x

Wende U-Substitution an

= \int_{0}^{\frac{π}{2}} sin (u) \cdot 2 u d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{\frac{π}{2}} sin (u) u d u

Wende die partielle Integration an

= 2 [- u cos (u) - \int - cos (u) d u]_{0}^{\frac{π}{2}}

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

= 2 [- u cos (u) - (- sin (u))]_{0}^{\frac{π}{2}}

Vereinfache

= 2 [- u cos (u) + sin (u)]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

sin (\frac{π}{2}) - \frac{π}{2} cos (\frac{π}{2})

= 2 (sin (\frac{π}{2}) - \frac{π}{2} cos (\frac{π}{2}))

Vereinfache

= 2 sin (\frac{π}{2}) - π cos (\frac{π}{2})

Graph

Beliebte Beispiele

integral from 0 to 1 of e^t+4te^t

\int_{0}^{1} e^{t} + 4 t e^{t} d t

integral from 0 to 1 of e^xln(x+1)

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

integral from-2 to 0 of 1/x

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

integral from 2 to 4 of 2/x

\int_{2}^{4} \frac{2}{x} d x

integral from-1 to 1 of |x-2|

\int_{- 1}^{1} ∣ x - 2 ∣ d x