integral from-7 to 1 of xsqrt(2-x)

Lösung

\int_{- 7}^{1} x 2 - x d x

- \frac{932}{15}

Dezimale

- 62.13333 \dots

Schritte zur Lösung

\int_{- 7}^{1} x 2 - x d x

Wende U-Substitution an

= \int_{9}^{1} - (- u + 2) u d u

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

= - \int_{1}^{9} - (- u + 2) u d u

Entferne die Konstante:

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

= - (- \int_{1}^{9} (- u + 2) u d u)

Multipliziere aus

(- u + 2) u : - u^{\frac{3}{2}} + 2 u

= - (- \int_{1}^{9} - u^{\frac{3}{2}} + 2 u d u)

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (- (- \int_{1}^{9} u^{\frac{3}{2}} d u + \int_{1}^{9} 2 u d u))

\int_{1}^{9} u^{\frac{3}{2}} d u = \frac{484}{5}

\int_{1}^{9} 2 u d u = \frac{104}{3}

= - (- (- \frac{484}{5} + \frac{104}{3}))

Vereinfache

- (- (- \frac{484}{5} + \frac{104}{3})) : - \frac{932}{15}

= - \frac{932}{15}

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