integral from 0 to 1 of 2pix(21-21x)

Lösung

\int_{0}^{1} 2 π x (21 - 21 x) d x

7 π

Dezimale

21.99114 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π x (21 - 21 x) d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{1} x (21 - 21 x) d x

Wende die partielle Integration an

= 2 π [\frac{1}{2} x^{2} (21 - 21 x) - \int - \frac{21 x ^{2}}{2} d x]_{0}^{1}

\int - \frac{21 x ^{2}}{2} d x = - \frac{7 x ^{3}}{2}

= 2 π [\frac{1}{2} x^{2} (21 - 21 x) - (- \frac{7 x ^{3}}{2})]_{0}^{1}

Vereinfache

2 π [\frac{1}{2} x^{2} (21 - 21 x) - (- \frac{7 x ^{3}}{2})]_{0}^{1} : 2 π [\frac{1}{2} (21 x^{2} - 14 x^{3})]_{0}^{1}

= 2 π [\frac{1}{2} (21 x^{2} - 14 x^{3})]_{0}^{1}

Berechne die Grenzen:

\frac{7}{2}

= 2 π \frac{7}{2}

Vereinfache

= 7 π

l a pl a ce t r an s f or m (t - 1) cos (4 t - 4)

\frac{\partial}{\partial x} (e^{- t} \cdot cos (π x))

\int x e^{y + 2 z} d y

d er i v a t i v e \frac{4 s}{s + 2}

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