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Beliebt Rechnen >

integral from 0 to 2 of sqrt(1+16x^2)

Lösung

\int_{0}^{2} 1 + 16 x^{2} d x

Lösung

65 + \frac{1}{8} ln (8 + 65)

+1

Dezimale

8.40931 \dots

Schritte zur Lösung

\int_{0}^{2} 1 + 16 x^{2} d x

Trigonometrische Substitution anwenden

= \int_{0}^{a r c t a n (8)} \frac{1}{4} sec^{3} (u) d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int_{0}^{a r c t a n (8)} sec^{3} (u) d u

Wende integrale Reduktion an

= \frac{1}{4} ([\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (8)} + \frac{1}{2} \cdot \int_{0}^{a r c t a n (8)} sec (u) d u)

\int_{0}^{a r c t a n (8)} sec (u) d u = ln (8 + 65)

= \frac{1}{4} ([\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (8)} + \frac{1}{2} ln (8 + 65))

Vereinfache

\frac{1}{4} ([\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (8)} + \frac{1}{2} ln (8 + 65)) : \frac{1}{4} ([\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (8)} + \frac{1}{2} ln (8 + 65))

= \frac{1}{4} ([\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (8)} + \frac{1}{2} ln (8 + 65))

Berechne die Grenzen:

465

= \frac{1}{4} (465 + \frac{1}{2} ln (8 + 65))

Vereinfache

= 65 + \frac{1}{8} ln (8 + 65)

Graph

Beliebte Beispiele

limit as x approaches pi of \sqrt[5]{(x-pi)/(x+pi)}

x \to π lim (5 \frac{x - π}{x + π})

vereinfachen 2pisqrt(x/g)

s im pl i f y 2 π \frac{x}{g}

derivative of (-ln(x+1)/(x^2))

\frac{d}{d x} (\frac{- ln ( x ) + 1}{x ^{2}})

derivative of (x^2-3/x)

\frac{d}{d x} (\frac{x ^{2} - 3}{x})

integral of (5t^2)/2

\int \frac{5 t ^{2}}{2} d t