integral from 0 to 2 of xsqrt(11-x^2)

Lösung

\int_{0}^{2} x 11 - x^{2} d x

\frac{11 11 - 7 7}{3}

Dezimale

5.98753 \dots

Schritte zur Lösung

\int_{0}^{2} x 11 - x^{2} d x

Wende U-Substitution an

= \int_{11}^{7} - \frac{u}{2} d u

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

= - \int_{7}^{11} - \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_{7}^{11} u d u)

Wende die Potenzregel an

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{11})

Vereinfache

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{7}^{11}

Berechne die Grenzen:

\frac{22 11 - 14 7}{3}

= \frac{1}{2} \cdot \frac{22 11 - 14 7}{3}

Vereinfache

= \frac{11 11 - 7 7}{3}

\int (x^{2} + 5) e^{- x} d x

2 y^{^{'}} + y = \frac{3}{2} t^{2}

x \to - 2 lim (\frac{2 x}{x + 2})

\frac{d}{d x} (11 x^{\frac{1}{2}} + x^{\frac{3}{2}})

\int_{- 6}^{- 2} (- x^{2} - 8 x - 18) d x