integral from 2 to 3 of sqrt(1+x^2)

Lösung

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

\frac{3 5}{2} - 5 + \frac{1}{2} (ln (3 + 10) - ln (2 + 5))

Dezimale

2.69475 \dots

Schritte zur Lösung

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

Trigonometrische Substitution anwenden

= \int_{a r c t a n (2)}^{a r c t a n (3)} sec^{3} (u) d u

Wende integrale Reduktion an

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{a r c t a n (2)}^{a r c t a n (3)} + \frac{1}{2} \cdot \int_{a r c t a n (2)}^{a r c t a n (3)} sec (u) d u

\int_{a r c t a n (2)}^{a r c t a n (3)} sec (u) d u = ln (3 + 10) - ln (2 + 5)

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{a r c t a n (2)}^{a r c t a n (3)} + \frac{1}{2} (ln (3 + 10) - ln (2 + 5))

Vereinfache

[\frac{sec ^{2} ( u ) sin ( u )}{2}]_{a r c t a n (2)}^{a r c t a n (3)} + \frac{1}{2} (ln (3 + 10) - ln (2 + 5)) : [\frac{1}{2} sec (u) tan (u)]_{a r c t a n (2)}^{a r c t a n (3)} + \frac{1}{2} (ln (3 + 10) - ln (2 + 5))

= [\frac{1}{2} sec (u) tan (u)]_{a r c t a n (2)}^{a r c t a n (3)} + \frac{1}{2} (ln (3 + 10) - ln (2 + 5))

Berechne die Grenzen:

\frac{3 5}{2} - 5

= \frac{3 5}{2} - 5 + \frac{1}{2} (ln (3 + 10) - ln (2 + 5))

\int_{0}^{\frac{1}{9}} x ln (9 x) d x

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