integral from 2 to 1 of-4x^{-3}

Lösung

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

\frac{3}{2}

Dezimale

1.5

Schritte zur Lösung

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Entferne die Konstante:

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

= - (- 4 \cdot \int_{1}^{2} x^{- 3} d x)

Wende die Potenzregel an

= - (- 4 [- \frac{1}{2 x ^{2}}]_{1}^{2})

Vereinfache

= 4 [- \frac{1}{2 x ^{2}}]_{1}^{2}

Berechne die Grenzen:

\frac{3}{8}

= 4 \cdot \frac{3}{8}

Vereinfache

= \frac{3}{2}

\int \frac{x ^{7}}{( 2 - x ^{8} ) ^{2}} d x

10000 y^{^{''}} - 81 y = 0, y (0) = 1, y^{^{'}} (0) = 3

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2}})

y^{^{'}} = - k y^{3}

\int (\frac{1}{x} + cot (x) - sec (x)) d x