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Beliebt Rechnen >

integral from 0 to 1 of (x^2+y^2+z^2)

Lösung

\int_{0}^{1} (x^{2} + y^{2} + z^{2}) d x

Lösung

y^{2} + z^{2} + \frac{1}{3}

Schritte zur Lösung

\int_{0}^{1} x^{2} + y^{2} + z^{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}^{1} y^{2} d x + \int_{0}^{1} z^{2} d x + \int_{0}^{1} x^{2} d x

\int_{0}^{1} y^{2} d x = y^{2}

\int_{0}^{1} z^{2} d x = z^{2}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= y^{2} + z^{2} + \frac{1}{3}

Beliebte Beispiele

integral of t^2e^{-6t}

\int t^{2} e^{- 6 t} d t

sum from n=1 to infinity of n!

n = 1 \sum \infty n!

derivative of 12x^3+6x^2+2x

\frac{d}{d x} (12 x^{3} + 6 x^{2} + 2 x)

derivative f(x)=sqrt(3x^2+2)

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

inverselaplace 7/(s^4)

in v erse l a pl a ce \frac{7}{s ^{4}}