de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 8 to 16 of xsqrt(16x-x^2)

Lösung

\int_{8}^{16} x 16 x - x^{2} d x

Lösung

\frac{512}{3} + 128 π

+1

Dezimale

572.79052 \dots

Schritte zur Lösung

\int_{8}^{16} x 16 x - x^{2} d x

Vervollständige das Quadrat

16 x - x^{2} : - (x - 8)^{2} + 64

= \int_{8}^{16} x - (x - 8)^{2} + 64 d x

Wende U-Substitution an

= \int_{0}^{8} (u + 8) - u^{2} + 64 d u

Multipliziere aus

(u + 8) - u^{2} + 64 : u - u^{2} + 64 + 8 - u^{2} + 64

= \int_{0}^{8} u - u^{2} + 64 + 8 - u^{2} + 64 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{8} u - u^{2} + 64 d u + \int_{0}^{8} 8 - u^{2} + 64 d u

\int_{0}^{8} u - u^{2} + 64 d u = \frac{512}{3}

\int_{0}^{8} 8 - u^{2} + 64 d u = 128 π

= \frac{512}{3} + 128 π

Graph

Beliebte Beispiele

derivative y=4-2x-x^{-3}

d er i v a t i v e y = 4 - 2 x - x^{- 3}

integral of r^2sec^2(r^3)

\int r^{2} sec^{2} (r^{3}) d r

tangent-6+250x^3-3x^5

t an g e n t - 6 + 250 x^{3} - 3 x^{5}

derivative of 1/(5x+1)

\frac{d}{d x} (\frac{1}{5 x + 1})

limit as x approaches-1f of x

x \to - 1 f lim (x)