integral from pi/2 to pi of sin(x)-x

Lösung

\int_{\frac{π}{2}}^{π} sin (x) - x d x

1 - \frac{3 π ^{2}}{8}

Dezimale

- 2.70110 \dots

Schritte zur Lösung

\int_{\frac{π}{2}}^{π} sin (x) - x d x

Wende die Summenregel an:

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

= \int_{\frac{π}{2}}^{π} sin (x) d x - \int_{\frac{π}{2}}^{π} x d x

\int_{\frac{π}{2}}^{π} sin (x) d x = 1

\int_{\frac{π}{2}}^{π} x d x = \frac{3 π ^{2}}{8}

= 1 - \frac{3 π ^{2}}{8}

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