integral from 1 to 2 of xsqrt(4-x^2)

Lösung

\int_{1}^{2} x 4 - x^{2} d x

3

Dezimale

1.73205 \dots

Schritte zur Lösung

\int_{1}^{2} x 4 - x^{2} d x

Wende U-Substitution an

= \int_{3}^{0} - \frac{u}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{3} - \frac{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}^{3} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{3})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{3}

Berechne die Grenzen:

23

= \frac{1}{2} \cdot 23

Vereinfache

= 3

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