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Beliebt Rechnen >

integral from 0 to 4 of 1/(sqrt(16+t^2))

Lösung

\int_{0}^{4} \frac{1}{16 + t ^{2}} d t

Lösung

ln (1 + 2)

+1

Dezimale

0.88137 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{1}{16 + t ^{2}} d t

Trigonometrische Substitution anwenden

= \int_{0}^{\frac{π}{4}} sec (u) d u

Nutze das gemeinsame Integral :

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

= [ln ∣ tan (u) + sec (u) ∣]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

ln (1 + 2)

= ln (1 + 2)

Graph

Beliebte Beispiele

integral of 8x(4x^2-3)^5

\int 8 x (4 x^{2} - 3)^{5} d x

integral of x/(x^2+4x+13)

\int \frac{x}{x ^{2} + 4 x + 13} d x

d er i v a t i v e 4 x

derivative G(t)=(1-4t)/(5+t)

d er i v a t i v e G (t) = \frac{1 - 4 t}{5 + t}

derivative of (-cos(2x)/2)

\frac{d}{d x} (\frac{- cos ( 2 x )}{2})