integral from 0 to 1/4 of 1/(1-x^2)

Lösung

\int_{0}^{\frac{1}{4}} \frac{1}{1 - x ^{2}} d x

\frac{ln ( \frac{5}{4} ) - ln ( \frac{3}{4} )}{2}

Dezimale

0.25541 \dots

Schritte zur Lösung

\int_{0}^{\frac{1}{4}} \frac{1}{1 - x ^{2}} d x

Nutze das gemeinsame Integral :

\int \frac{1}{1 - x ^{2}} d x = \frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}

= [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{0}^{\frac{1}{4}}

Vereinfache

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{0}^{\frac{1}{4}} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{0}^{\frac{1}{4}}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{0}^{\frac{1}{4}}

Berechne die Grenzen:

\frac{ln ( \frac{5}{4} ) - ln ( \frac{3}{4} )}{2}

= \frac{ln ( \frac{5}{4} ) - ln ( \frac{3}{4} )}{2}

\int_{x}^{1} \frac{6}{7} x + \frac{12}{7} y d y

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

\int_{- π}^{π} x sin (n) x d x

\int_{3}^{4} 5 d x

\int_{3}^{5} x - 3 d x