integral from-3 to-2 of 2x(4-x^2)^3

Lösung

\int_{- 3}^{- 2} 2 x (4 - x^{2})^{3} d x

\frac{625}{4}

Dezimale

156.25

Schritte zur Lösung

\int_{- 3}^{- 2} 2 x (4 - x^{2})^{3} d x

Entferne die Konstante:

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

= 2 \cdot \int_{- 3}^{- 2} x (4 - x^{2})^{3} d x

Wende U-Substitution an

= 2 \cdot \int_{- 5}^{0} - \frac{u ^{3}}{2} d u

Entferne die Konstante:

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

= 2 (- \frac{1}{2} \cdot \int_{- 5}^{0} u^{3} d u)

Wende die Potenzregel an

= 2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 5}^{0})

Vereinfache

2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 5}^{0}) : - [\frac{u ^{4}}{4}]_{- 5}^{0}

= - [\frac{u ^{4}}{4}]_{- 5}^{0}

Berechne die Grenzen:

- \frac{625}{4}

= - (- \frac{625}{4})

Vereinfache

= \frac{625}{4}

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

\int \frac{1}{( 3 - x ) 2 - x} d x

\frac{\partial}{\partial y} (x^{2} + x y + y^{2} + y)

d er i v a t i v e f (x) = (3 x^{3} + 1)^{2}

x \to - 8 - lim (x^{2} + \frac{2}{x + 8})