integral from 1 to 7 of |sin(x)|

Lösung

\int_{1}^{7} ∣ sin (x) ∣ d x

4 + cos (1) - cos (7)

Dezimale

3.78640 \dots

Schritte zur Lösung

\int_{1}^{7} ∣ sin (x) ∣ d x

Entferne die Extremwerte

= \int_{1}^{π} sin (x) d x + \int_{π}^{2 π} - sin (x) d x + \int_{2 π}^{7} sin (x) d x

\int_{1}^{π} sin (x) d x = 1 + cos (1)

\int_{π}^{2 π} - sin (x) d x = 2

\int_{2 π}^{7} sin (x) d x = - cos (7) + 1

= 1 + cos (1) + 2 - cos (7) + 1

Vereinfache

= 4 + cos (1) - cos (7)

\int_{0}^{1} (1 - x) sin (nπ x) d x

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

\int_{2}^{3} \frac{x}{1 - x ^{2}} d x

\int_{2}^{6} x d x

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