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Beliebt Rechnen >

integral from-5 to 5 of sqrt(1+x^2)

Lösung

\int_{- 5}^{5} 1 + x^{2} d x

Lösung

526 + \frac{1}{2} (ln (5 + 26) - ln (- 5 + 26))

+1

Dezimale

27.80753 \dots

Schritte zur Lösung

\int_{- 5}^{5} 1 + x^{2} d x

Trigonometrische Substitution anwenden

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

Wende integrale Reduktion an

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

\int_{- a r c t a n (5)}^{a r c t a n (5)} sec (u) d u = ln (5 + 26) - ln (- 5 + 26)

= [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (5)}^{a r c t a n (5)} + \frac{1}{2} (ln (5 + 26) - ln (- 5 + 26))

Vereinfache

[\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (5)}^{a r c t a n (5)} + \frac{1}{2} (ln (5 + 26) - ln (- 5 + 26)) : [\frac{1}{2} sec (u) tan (u)]_{- a r c t a n (5)}^{a r c t a n (5)} + \frac{1}{2} (ln (5 + 26) - ln (- 5 + 26))

= [\frac{1}{2} sec (u) tan (u)]_{- a r c t a n (5)}^{a r c t a n (5)} + \frac{1}{2} (ln (5 + 26) - ln (- 5 + 26))

Berechne die Grenzen:

526

= 526 + \frac{1}{2} (ln (5 + 26) - ln (- 5 + 26))

Graph

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