de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

\int_{- 2}^{2} 1 + 4 x^{2} d x

Lösung

\frac{1}{2} (417 + \frac{1}{2} (ln (4 + 17) - ln (- 4 + 17)))

+1

Dezimale

9.29356 \dots

Schritte zur Lösung

\int_{- 2}^{2} 1 + 4 x^{2} d x

Trigonometrische Substitution anwenden

= \int_{- a r c t a n (4)}^{a r c t a n (4)} \frac{1}{2} sec^{3} (u) d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- a r c t a n (4)}^{a r c t a n (4)} sec^{3} (u) d u

Wende integrale Reduktion an

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

\int_{- a r c t a n (4)}^{a r c t a n (4)} sec (u) d u = ln (4 + 17) - ln (- 4 + 17)

= \frac{1}{2} ([\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (4)}^{a r c t a n (4)} + \frac{1}{2} (ln (4 + 17) - ln (- 4 + 17)))

Vereinfache

\frac{1}{2} ([\frac{sec ^{2} ( u ) sin ( u )}{2}]_{- a r c t a n (4)}^{a r c t a n (4)} + \frac{1}{2} (ln (4 + 17) - ln (- 4 + 17))) : \frac{1}{2} ([\frac{1}{2} sec (u) tan (u)]_{- a r c t a n (4)}^{a r c t a n (4)} + \frac{1}{2} (ln (4 + 17) - ln (- 4 + 17)))

= \frac{1}{2} ([\frac{1}{2} sec (u) tan (u)]_{- a r c t a n (4)}^{a r c t a n (4)} + \frac{1}{2} (ln (4 + 17) - ln (- 4 + 17)))

Berechne die Grenzen:

417

= \frac{1}{2} (417 + \frac{1}{2} (ln (4 + 17) - ln (- 4 + 17)))

Graph

Beliebte Beispiele

fläche y=sqrt(x),y= 1/3 x

a re a y = x, y = \frac{1}{3} x

sum from n=4 to infinity}(\sqrt{n of)/(n-3)

n = 4 \sum \infty \frac{n}{n - 3}

(dy)/(dx)-e^{2x+y}=0

\frac{d y}{d x} - e^{2 x + y} = 0

derivative of ax^3+bx^2+cx

\frac{d}{d x} (a x^{3} + b x^{2} + c x)

(\partial ^2)/(\partial x\partial y)(x^2-e^{y^2})

\frac{\partial ^{2}}{\partial x \partial y} (x^{2} - e^{y^{2}})