integral from-pi/4 to pi/4 of x^3sin(x)

Lösung

\int_{- \frac{π}{4}}^{\frac{π}{4}} x^{3} sin (x) d x

\frac{3 π}{2} - \frac{π ^{3}}{32 2} + \frac{3 π ^{2}}{8 2} - 62

Dezimale

0.11096 \dots

Schritte zur Lösung

\int_{- \frac{π}{4}}^{\frac{π}{4}} x^{3} sin (x) d x

Wende die partielle Integration an

= [- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x]_{- \frac{π}{4}}^{\frac{π}{4}}

\int - 3 x^{2} cos (x) d x = - 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))

= [- x^{3} cos (x) - (- 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))]_{- \frac{π}{4}}^{\frac{π}{4}}

Vereinfache

= [- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))]_{- \frac{π}{4}}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{3 π}{2} - \frac{π ^{3}}{32 2} + \frac{3 π ^{2}}{8 2} - 62

= \frac{3 π}{2} - \frac{π ^{3}}{32 2} + \frac{3 π ^{2}}{8 2} - 62

\int_{0}^{2} \frac{1}{4 - s ^{2}} d s

\int_{1}^{3} x^{2} - 4 d x

\int_{0}^{3} (5 x^{2} + 9 x) d x

\int_{\frac{π}{6}}^{\frac{π}{3}} csc (x) d x

\int_{1}^{3 x^{2}} \frac{sin ( t )}{t} d t