integral from-1 to 1 of x-3+1/(x-2)

Lösung

\int_{- 1}^{1} x - 3 + \frac{1}{x - 2} d x

- ln (3) - 6

Dezimale

- 7.09861 \dots

Schritte zur Lösung

\int_{- 1}^{1} x - 3 + \frac{1}{x - 2} 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

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

\int_{- 1}^{1} x d x = 0

\int_{- 1}^{1} 3 d x = 6

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

= 0 - 6 - ln (3)

Vereinfache

= - ln (3) - 6

\int_{0}^{1} 3.6 x^{3} - 2.4 x^{4} d x

\int_{50}^{100} 7 x d x

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\int_{- 1}^{2} - x^{2} - x + 8 d x

\int_{1}^{6} \frac{1}{( x - 5 ) ^{2}} d x