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Beliebt Rechnen >

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

Lösung

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

Lösung

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

+1

Dezimale

11.30527 \dots

Schritte zur Lösung

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

Trigonometrische Substitution anwenden

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

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

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

Vereinfache

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

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

Berechne die Grenzen:

310

= 310 + \frac{1}{2} (ln (3 + 10) - ln (- 3 + 10))

Graph

Beliebte Beispiele

implicit (dy)/(dx),y-9x^3+8=0,(2,8)

im pl i c i t \frac{d y}{d x}, y - 9 x^{3} + 8 = 0, (2, 8)

derivative 4^{x^2}

d er i v a t i v e 4^{x^{2}}

integral of (csc(2x))

\int (csc (2 x)) d x

y^'-2ty=12t^2e^{t^2},y(0)=5

y^{^{'}} - 2 t y = 12 t^{2} e^{t^{2}}, y (0) = 5

limit as x approaches 4 of (x^2-4)/(x-2)

x \to 4 lim (\frac{x ^{2} - 4}{x - 2})