integral from 0 to 1 of-2xsqrt(9-x^2)

Lösung

\int_{0}^{1} - 2 x 9 - x^{2} d x

- 18 + \frac{32 2}{3}

Dezimale

- 2.91505 \dots

Schritte zur Lösung

\int_{0}^{1} - 2 x 9 - x^{2} d x

Entferne die Konstante:

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

= - 2 \cdot \int_{0}^{1} x 9 - x^{2} d x

Wende U-Substitution an

= - 2 \cdot \int_{9}^{8} - \frac{u}{2} d u

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

= - 2 (- \int_{8}^{9} - \frac{u}{2} d u)

Entferne die Konstante:

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

= - 2 (- (- \frac{1}{2} \cdot \int_{8}^{9} u d u))

Wende die Potenzregel an

= - 2 (- (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{9}))

Vereinfache

- 2 (- (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{9})) : - [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{9}

= - [\frac{2}{3} u^{\frac{3}{2}}]_{8}^{9}

Berechne die Grenzen:

18 - \frac{32 2}{3}

= - (18 - \frac{32 2}{3})

Vereinfache

= - 18 + \frac{32 2}{3}

\int_{0}^{π} t sin (t) d t

\int_{0}^{1} t^{2} e^{- s t} d t

\int_{0}^{a r c s i n (x)} cos (x) d x

\int_{- 3}^{4} ∣ x + 2 ∣ d x

\int_{0}^{l n (π)} e^{x} cos (e^{x}) d x