integral from 0 to 4 of 6x-x^2

Lösung

\int_{0}^{4} 6 x - x^{2} d x

\frac{80}{3}

Dezimale

26.66666 \dots

Schritte zur Lösung

\int_{0}^{4} 6 x - 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

= \int_{0}^{4} 6 x d x - \int_{0}^{4} x^{2} d x

\int_{0}^{4} 6 x d x = 48

\int_{0}^{4} x^{2} d x = \frac{64}{3}

= 48 - \frac{64}{3}

Vereinfache

48 - \frac{64}{3} : \frac{80}{3}

= \frac{80}{3}

\frac{d y}{d x} = (x - 5) e^{- 2 y}, y (5) = ln (5)

\int \frac{3 x ^{2}}{49 - x ^{2}} d x

\int \frac{e ^{y}}{( e ^{y} + 1 ) ^{2}} d y

y^{^{'}} = \frac{y \cdot e ^{x}}{x}

\int_{3}^{4} \frac{x}{x ^{2} + 4 x + 20} d x