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

Lösung

\int_{- 1}^{1} ∣ x ∣ sin (x) d x

0

Schritte zur Lösung

\int_{- 1}^{1} ∣ x ∣ sin (x) d x

Entferne die Extremwerte

= \int_{- 1}^{0} (- x) sin (x) d x + \int_{0}^{1} x sin (x) d x

\int_{- 1}^{0} (- x) sin (x) d x = - sin (1) + cos (1)

\int_{0}^{1} x sin (x) d x = sin (1) - cos (1)

= - sin (1) + cos (1) + sin (1) - cos (1)

Vereinfache

= 0

\int_{0}^{\frac{π}{2}} x sin (3 x) d x

\int_{0}^{4 π} ∣ sin (x) ∣ d x

\int_{0}^{2} 4 t^{2} + 1 d t

\int_{x}^{3} 1 d x

\int_{0}^{2} (2 x^{2} - 4 x) d x