integral from-2 to 2 of (10)/(x^2-2x-24)

Lösung

\int_{- 2}^{2} \frac{10}{x ^{2} - 2 x - 24} d x

- ln (3) - ln (2)

Dezimale

- 1.79175 \dots

Schritte zur Lösung

\int_{- 2}^{2} \frac{10}{x ^{2} - 2 x - 24} d x

Entferne die Konstante:

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

= 10 \cdot \int_{- 2}^{2} \frac{1}{x ^{2} - 2 x - 24} d x

Ermittle den Partialbruch von

\frac{1}{x ^{2} - 2 x - 24} : - \frac{1}{10 ( x + 4 )} + \frac{1}{10 ( x - 6 )}

= 10 \cdot \int_{- 2}^{2} - \frac{1}{10 ( x + 4 )} + \frac{1}{10 ( x - 6 )} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 10 (- \int_{- 2}^{2} \frac{1}{10 ( x + 4 )} d x + \int_{- 2}^{2} \frac{1}{10 ( x - 6 )} d x)

\int_{- 2}^{2} \frac{1}{10 ( x + 4 )} d x = \frac{1}{10} ln (3)

\int_{- 2}^{2} \frac{1}{10 ( x - 6 )} d x = - \frac{1}{10} ln (2)

= 10 (- \frac{1}{10} ln (3) - \frac{1}{10} ln (2))

Vereinfache

10 (- \frac{1}{10} ln (3) - \frac{1}{10} ln (2)) : - ln (3) - ln (2)

= - ln (3) - ln (2)

f (x) = 1 - 2 cos (x)

\int cot (\frac{x}{9}) d x

d er i v a t i v e \frac{x}{( x ^{2} + 3 x ) ^{5}}

x \to \infty lim (x n (x))

t an g e n t f (x) = x^{4} - 3 x^{2} + 2, at x = 1