de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 0 to 2pi of sqrt(20+16t^2)

Lösung

\int_{0}^{2 π} 20 + 16 t^{2} d t

Lösung

2 π 16 π^{2} + 5 + \frac{5}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

+1

Dezimale

86.26528 \dots

Schritte zur Lösung

\int_{0}^{2 π} 20 + 16 t^{2} d t

Trigonometrische Substitution anwenden

= \int_{0}^{a r c t a n (\frac{4 π}{5})} 5 sec^{3} (u) d u

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{a r c t a n (\frac{4 π}{5})} sec^{3} (u) d u

Wende integrale Reduktion an

= 5 [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (\frac{4 π}{5})} + \frac{1}{2} \cdot \int_{0}^{a r c t a n (\frac{4 π}{5})} sec (u) d u

\int_{0}^{a r c t a n (\frac{4 π}{5})} sec (u) d u = ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

= 5 [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (\frac{4 π}{5})} + \frac{1}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

Vereinfache

5 [\frac{sec ^{2} ( u ) sin ( u )}{2}]_{0}^{a r c t a n (\frac{4 π}{5})} + \frac{1}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1) : 5 [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (\frac{4 π}{5})} + \frac{5}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

= 5 [\frac{1}{2} sec (u) tan (u)]_{0}^{a r c t a n (\frac{4 π}{5})} + \frac{5}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

Berechne die Grenzen:

\frac{2 π 16 π ^{2} + 5}{5}

= 5 \cdot \frac{2 π 16 π ^{2} + 5}{5} + \frac{5}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

Vereinfache

= 2 π 16 π^{2} + 5 + \frac{5}{2} ln (\frac{4 π}{5} + \frac{16 π ^{2}}{5} + 1)

Graph

Beliebte Beispiele

limit as x approaches-2 of (x+1)^4(2x^2)

x \to - 2 lim ((x + 1)^{4} (2 x^{2}))

derivative (x^2+9)/(x+3)

d er i v a t i v e \frac{x ^{2} + 9}{x + 3}

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

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

tangent f(x)= 2/(x+1),\at x=1

t an g e n t f (x) = \frac{2}{x + 1}, at x = 1

x y^{^{'}} - 2 y = 11 x^{2}