fläche y=28-x^2,y=3x,y= 3/5 x

Lösung

fläche

y = 28 - x^{2}, y = 3 x, y = \frac{3}{5} x

\frac{8958}{125}

Dezimale

71.664

Schritte zur Lösung

Um die Schnittpunkte zu finden, löse

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

28 - x^{2} = 3 x : x = - 7, x = 4

28 - x^{2} = \frac{3}{5} x : x = - \frac{28}{5}, x = 5

3 x = \frac{3}{5} x : x = 0

= \int_{- 7}^{- \frac{28}{5}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{- \frac{28}{5}}^{0} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{0}^{4} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{4}^{5} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 7}^{- \frac{28}{5}} 28 - x^{2} - 3 x d x + \int_{- \frac{28}{5}}^{0} 3 x - \frac{3}{5} x d x + \int_{0}^{4} 3 x - \frac{3}{5} x d x + \int_{4}^{5} 28 - x^{2} - \frac{3}{5} x d x

\int_{- 7}^{- \frac{28}{5}} 28 - x^{2} - 3 x d x = \frac{7399}{750}

\int_{- \frac{28}{5}}^{0} 3 x - \frac{3}{5} x d x = \frac{4704}{125}

\int_{0}^{4} 3 x - \frac{3}{5} x d x = \frac{96}{5}

\int_{4}^{5} 28 - x^{2} - \frac{3}{5} x d x = \frac{149}{30}

= \frac{7399}{750} + \frac{4704}{125} + \frac{96}{5} + \frac{149}{30}

Vereinfache

= \frac{8958}{125}

\int (\frac{16}{2} x^{3} + 12 x^{5} - 2 x + 1) d x

d er i v a t i v e f (x) = 5 e^{x} (cos (x) - sin (x))

\frac{\partial}{\partial x} ((x^{2} + y^{2})^{0.5})

y^{^{''}} = 1

d er i v a t i v e f (2) = x^{3} - 2 x