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Beliebt Rechnen >

integral from 0 to pi/2 of xcos(x^2)

Lösung

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

Lösung

\frac{1}{2} sin (\frac{π ^{2}}{4})

+1

Dezimale

0.31213 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{\frac{π ^{2}}{4}} \frac{cos ( u )}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π ^{2}}{4}} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [sin (u)]_{0}^{\frac{π ^{2}}{4}}

Berechne die Grenzen:

sin (\frac{π ^{2}}{4})

= \frac{1}{2} sin (\frac{π ^{2}}{4})

Graph

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