integral from 0 to 3pi of 2x^2sin(1/6 x)

Lösung

\int_{0}^{3 π} 2 x^{2} sin (\frac{1}{6} x) d x

432 (π - 2)

Dezimale

493.16802 \dots

Schritte zur Lösung

\int_{0}^{3 π} 2 x^{2} sin (\frac{1}{6} x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{3 π} x^{2} sin (\frac{1}{6} x) d x

Wende U-Substitution an

= 2 \cdot \int_{0}^{\frac{π}{2}} 216 u^{2} sin (u) d u

Entferne die Konstante:

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

= 2 \cdot 216 \cdot \int_{0}^{\frac{π}{2}} u^{2} sin (u) d u

Wende die partielle Integration an

= 2 \cdot 216 [- u^{2} cos (u) - \int - 2 u cos (u) d u]_{0}^{\frac{π}{2}}

\int - 2 u cos (u) d u = - 2 (u sin (u) + cos (u))

= 2 \cdot 216 [- u^{2} cos (u) - (- 2 (u sin (u) + cos (u)))]_{0}^{\frac{π}{2}}

Vereinfache

= 432 [- u^{2} cos (u) + 2 (u sin (u) + cos (u))]_{0}^{\frac{π}{2}}

Berechne die Grenzen:

π - 2

= 432 (π - 2)

\frac{d}{d x} (\frac{e ^{x} + 1}{x ^{2}})

\frac{d}{d x} (6 x^{4} - 2 x^{3} - 12 x^{2} + 3 x + 3)

\frac{d ^{2}}{d x ^{2}} (\frac{4}{5 t ^{6}})

d er i v a t i v e e^{2 - x}

y^{^{'}} = 23 x y