integral from 0 to 1 of x^2cos(pi/2 x^3)

Lösung

\int_{0}^{1} x^{2} cos (\frac{π}{2} x^{3}) d x

\frac{2}{3 π}

Dezimale

0.21220 \dots

Schritte zur Lösung

\int_{0}^{1} x^{2} cos (\frac{π}{2} x^{3}) d x

Wende U-Substitution an

= \int_{0}^{1} \frac{cos ( \frac{π u}{2} )}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{0}^{1} cos (\frac{π u}{2}) d u

Wende U-Substitution an

= \frac{1}{3} \cdot \int_{0}^{\frac{π}{2}} cos (v) \frac{2}{π} d v

Entferne die Konstante:

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

= \frac{1}{3} \cdot \frac{2}{π} \cdot \int_{0}^{\frac{π}{2}} cos (v) d v

Nutze das gemeinsame Integral :

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

= \frac{1}{3} \cdot \frac{2}{π} [sin (v)]_{0}^{\frac{π}{2}}

Vereinfache

\frac{1}{3} \cdot \frac{2}{π} [sin (v)]_{0}^{\frac{π}{2}} : \frac{2}{3 π} [sin (v)]_{0}^{\frac{π}{2}}

= \frac{2}{3 π} [sin (v)]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

1

= \frac{2}{3 π} \cdot 1

Vereinfache

= \frac{2}{3 π}

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