integral from 1.5 to 2.5 of 9800(7-y)(1)

Lösung

\int_{1.5}^{2.5} 9800 (7 - y) (1) d y

49000

Schritte zur Lösung

\int_{1.5}^{2.5} 9800 (7 - y) \cdot 1 d y

Entferne die Konstante:

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

= 9800 \cdot 1 \cdot \int_{1.5}^{2.5} 7 - y d y

Vereinfache

= 9800 \cdot \int_{1.5}^{2.5} 7 - y d y

Wende die Summenregel an:

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

= 9800 (\int_{1.5}^{2.5} 7 d y - \int_{1.5}^{2.5} y d y)

\int_{1.5}^{2.5} 7 d y = 7

\int_{1.5}^{2.5} y d y = 2

= 9800 (7 - 2)

Vereinfache

= 49000

in v erse l a pl a ce \frac{1}{s ^{2} + 16}

in v erse l a pl a ce \frac{1}{s ( s ^{2} + s + \frac{5}{4} )}

d er i v a t i v e e^{x - 1}

\frac{\partial}{\partial x} (2 x y + 5 x^{2})

t an g e n t f (x) = \frac{x ^{2}}{x + 9}, at x = 1