integral from 3 to 7 of 1/(sqrt(x^2-4))

Lösung

\int_{3}^{7} \frac{1}{x ^{2} - 4} d x

ln (\frac{3 5}{2} + \frac{7}{2}) - ln (\frac{5}{2} + \frac{3}{2})

Dezimale

0.96242 \dots

Schritte zur Lösung

\int_{3}^{7} \frac{1}{x ^{2} - 4} d x

Trigonometrische Substitution anwenden

= \int_{arcsec (\frac{3}{2})}^{arcsec (\frac{7}{2})} sec (u) d u

Nutze das gemeinsame Integral :

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= [ln ∣ tan (u) + sec (u) ∣]_{arcsec (\frac{3}{2})}^{arcsec (\frac{7}{2})}

Berechne die Grenzen:

ln (\frac{3 5}{2} + \frac{7}{2}) - ln (\frac{5}{2} + \frac{3}{2})

= ln (\frac{3 5}{2} + \frac{7}{2}) - ln (\frac{5}{2} + \frac{3}{2})

\int_{0}^{1} \frac{e ^{- x}}{x + 1} d x

\int_{0}^{2} 5 t d t

\int_{0}^{3} \frac{x}{1 + 4 x ^{2}} d x

\int_{4}^{8} 8 - x d x

\int_{0}^{3} x^{3} e^{x^{4}} d x