integral from-1 to 3 of (-x^3+3x^2+1)

Lösung

\int_{- 1}^{3} (- x^{3} + 3 x^{2} + 1) d x

12

Schritte zur Lösung

\int_{- 1}^{3} - x^{3} + 3 x^{2} + 1 d x

Wende die Summenregel an:

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

= - \int_{- 1}^{3} x^{3} d x + \int_{- 1}^{3} 3 x^{2} d x + \int_{- 1}^{3} 1 d x

\int_{- 1}^{3} x^{3} d x = 20

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} 1 d x = 4

= - 20 + 28 + 4

Vereinfache

= 12

im pl i c i t \frac{- 8 x}{y} = 0

x \to 1 lim (x^{3} (5 - x))

x \to 1 lim (x^{\frac{1}{1 - x}})

n = 1 \sum \infty n (\frac{2}{3})^{n}

a re a y = sin (x), y = x, x = \frac{π}{2}, x = π