integral from-2 to 3 of (x^2-12)-(x-6)

Lösung

\int_{- 2}^{3} (x^{2} - 12) - (x - 6) d x

- \frac{125}{6}

Dezimale

- 20.83333 \dots

Schritte zur Lösung

\int_{- 2}^{3} x^{2} - 12 - (x - 6) d x

Vereinfache

= \int_{- 2}^{3} x^{2} - x - 6 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_{- 2}^{3} x^{2} d x - \int_{- 2}^{3} x d x - \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

\int_{- 2}^{3} x d x = \frac{5}{2}

\int_{- 2}^{3} 6 d x = 30

= \frac{35}{3} - \frac{5}{2} - 30

Vereinfache

\frac{35}{3} - \frac{5}{2} - 30 : - \frac{125}{6}

= - \frac{125}{6}

x \to 1 lim (x - 1)

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

x \to - 1 lim (x ∣ x - 4 ∣)

\int \frac{t ^{2}}{2 1 - t ^{2}} d t

t^{2} y^{^{'}} + 4 t y - y^{3} = 0, y (1) = \frac{3}{2}