integral from-8 to 8 of 1/2 (64-x^2)

Lösung

\int_{- 8}^{8} \frac{1}{2} (64 - x^{2}) d x

\frac{1024}{3}

Dezimale

341.33333 \dots

Schritte zur Lösung

\int_{- 8}^{8} \frac{1}{2} (64 - x^{2}) d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- 8}^{8} 64 - 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}{2} (\int_{- 8}^{8} 64 d x - \int_{- 8}^{8} x^{2} d x)

\int_{- 8}^{8} 64 d x = 1024

\int_{- 8}^{8} x^{2} d x = \frac{1024}{3}

= \frac{1}{2} (1024 - \frac{1024}{3})

Vereinfache

\frac{1}{2} (1024 - \frac{1024}{3}) : \frac{1024}{3}

= \frac{1024}{3}

n = 1 \sum \infty \frac{8}{n ^{4}}

y^{^{'}} sin (x) + y cos (x) = 0

d er i v a t i v e 147.456 π t

\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x y^{- 3} + 5 x + 3 y + 11)

t \to 5 lim (\frac{1}{t ^{2} - 4 t - 5} - \frac{1}{6 ( t - 5 )})