integral from 0 to 1 of 2pix(sqrt(x))

Lösung

\int_{0}^{1} 2 π x (x) d x

\frac{4 π}{5}

Dezimale

2.51327 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π x x d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{1} x x d x

Vereinfache

x x : x^{\frac{3}{2}}

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

Wende die Potenzregel an

= 2 π [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{1}

Berechne die Grenzen:

\frac{2}{5}

= 2 π \frac{2}{5}

Vereinfache

= \frac{4 π}{5}

\int \frac{2}{9} \frac{x ^{2}}{x ^{5}} d x

\int \frac{1}{( x + 1 ) ( x + 2 ) ( x + 3 )} d x

\frac{\partial}{\partial x} (9 - x^{2} + x y - 4 y^{2})

\int \frac{1}{cos ( x ) - 1} d x

x \to 0 lim (\frac{5 ^{x} - 1}{x})