integral from 1/2 to 1/3 of cos(pi)x

Lösung

\int_{\frac{1}{2}}^{\frac{1}{3}} cos (π) x d x

\frac{5}{72}

Dezimale

0.06944 \dots

Schritte zur Lösung

\int_{\frac{1}{2}}^{\frac{1}{3}} cos (π) x d x

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

= - \int_{\frac{1}{3}}^{\frac{1}{2}} cos (π) x d x

Entferne die Konstante:

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

= - cos (π) \cdot \int_{\frac{1}{3}}^{\frac{1}{2}} x d x

cos (π) = - 1

= - (- 1) \cdot \int_{\frac{1}{3}}^{\frac{1}{2}} x d x

Wende die Potenzregel an

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

Vereinfache

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

Berechne die Grenzen:

\frac{5}{72}

= \frac{5}{72}

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