integral from a to b of x^2(1/(b-a))

Lösung

\int_{a}^{b} x^{2} (\frac{1}{b - a}) d x

\frac{b ^{2} + ba + a ^{2}}{3}

Schritte zur Lösung

\int_{a}^{b} x^{2} \frac{1}{b - a} d x

Entferne die Konstante:

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

= \frac{1}{b - a} \cdot \int_{a}^{b} x^{2} d x

Wende die Potenzregel an

= \frac{1}{b - a} [\frac{x ^{3}}{3}]_{a}^{b}

Vereinfache

\frac{1}{b - a} [\frac{x ^{3}}{3}]_{a}^{b} : \frac{[ \frac{x ^{3}}{3} ] _{a}^{b}}{b - a}

= \frac{[ \frac{x ^{3}}{3} ] _{a}^{b}}{b - a}

Berechne die Grenzen:

\frac{b ^{3}}{3} - \frac{a ^{3}}{3}

= \frac{\frac{b ^{3}}{3} - \frac{a ^{3}}{3}}{b - a}

Vereinfache

= \frac{b ^{2} + ba + a ^{2}}{3}

d er i v a t i v e (x + 3)^{3 x - 2}

t an g e n t y = \frac{1}{x - 5}, (4, - 1)

\frac{d}{d y} (\frac{1}{y} e^{x y})

y^{2} = (x y y^{^{'}} + 1) ln (x)

y^{^{'}} = 1 - y