fläche x^2-11,10x,[-sqrt(11),0]y=0

Lösung

fläche

x^{2} - 11, 10 x, [- 11, 0] y = 0

\frac{830}{3}

Dezimale

276.66666 \dots

Schritte zur Lösung

Stelle

y

nach

[- 11, 0] y = 0

um:

y = 0

f_{1} (x) = 0

f_{2} (x) = x^{2} - 11

Um die Schnittpunkte zu finden, löse

f_{i} (x) = f_{j} (x)

0 = x^{2} - 11 : x = 11, x = - 11

0 = 10 x : x = 0

x^{2} - 11 = 10 x : x = 11, x = - 1

= \int_{- 11}^{- 1} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- 1}^{0} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{0}^{11} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{11}^{11} ∣ f_{3} (x) - f_{2} (x) ∣ d x

= \int_{- 11}^{- 1} 0 - (x^{2} - 11) d x + \int_{- 1}^{0} ∣ 0 - 10 x ∣ d x + \int_{0}^{11} ∣ 0 - 10 x ∣ d x + \int_{11}^{11} 10 x - (x^{2} - 11) d x

\int_{- 11}^{- 1} 0 - (x^{2} - 11) d x = - \frac{11 11 - 1}{3} - 11 + 1111

\int_{- 1}^{0} ∣ 0 - 10 x ∣ d x = 5

\int_{0}^{11} ∣ 0 - 10 x ∣ d x = 55

\int_{11}^{11} 10 x - (x^{2} - 11) d x = - \frac{1331 - 11 11}{3} + 671 - 1111

= - \frac{11 11 - 1}{3} - 11 + 1111 + 5 + 55 - \frac{1331 - 11 11}{3} + 671 - 1111

Vereinfache

= \frac{830}{3}

\frac{d}{d x} (- 1 0^{3 x^{2} - 4})

\frac{d}{d x} (\frac{2}{4 x ^{3}})

x \frac{d y}{d x} = e^{y + x}

t an g e n t x^{2} + 2 x y - y^{2} + x = 27, (4, 7)

\frac{d y}{d x} = \frac{y ^{3}}{1 - 2 x y ^{2}}, y (0) = 1