integral from 0 to-0.5 of 70x

Lösung

\int_{0}^{- 0.5} 70 x d x

8.75

Schritte zur Lösung

\int_{0}^{- 0.5} 70 x d x

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

= - \int_{- 0.5}^{0} 70 x d x

Entferne die Konstante:

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

= - 70 \cdot \int_{- 0.5}^{0} x d x

Wende die Potenzregel an

= - 70 [\frac{x ^{2}}{2}]_{- 0.5}^{0}

Vereinfache

= - 70 [0.5 x^{2}]_{- 0.5}^{0}

Berechne die Grenzen:

- 0.125

= - 70 (- 0.125)

Vereinfache

= 8.75

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