integral from 0 to 6 of (36-x^2)/(144)

Lösung

\int_{0}^{6} \frac{36 - x ^{2}}{144} d x

1

Schritte zur Lösung

\int_{0}^{6} \frac{36 - x ^{2}}{144} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{144} \cdot \int_{0}^{6} 36 - x^{2} 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

= \frac{1}{144} (\int_{0}^{6} 36 d x - \int_{0}^{6} x^{2} d x)

\int_{0}^{6} 36 d x = 216

\int_{0}^{6} x^{2} d x = 72

= \frac{1}{144} (216 - 72)

Vereinfache

\frac{1}{144} (216 - 72) : 1

= 1

\int_{0}^{50} q^{2} - 50 q + 700 d q

\int_{1}^{7} (12 - ∣ x - 4 ∣)^{2} d x

\int_{6}^{8} (\frac{1}{x ^{2}}) d x

\int_{0}^{1} 4 y^{2} d y

\int_{4}^{x^{2}} (3 t^{2} + 2 t) d t