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Flächeninhalt des Umdrehungsrechners

Berechnung des Flächeninhalts einer Rotationsfläche Schritt für Schritt

Der Rechner ermittelt den Flächeninhalt der Rotationsfläche (um die gegebene Achse) der expliziten, polaren oder parametrischen Kurve auf dem gegebenen Intervall, wobei die Schritte angezeigt werden.

Choose type:

Enter a function:

Rotate around the -axis

Enter a lower limit:

If you need , type -inf.

Enter an upper limit:

If you need , type inf.

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Solution

Your input: find the area of the surface of revolution of f(x)=x2 rotated about the x-axis on [0,1]

The surface area of the curve is given by S=2πbaf(x)(f(x))2+1dx

First, find the derivative: f(x)=(x2)=2x (steps can be seen here)

Finally, calculate the integral S=102πx2(2x)2+1dx=102πx24x2+1dx

The calculations and the answer for the integral can be seen here.