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Pole powierzchni obrotu Kalkulator

Obliczanie pola powierzchni obrotu krok po kroku

Kalkulator znajdzie pole powierzchni obrotu (wokół danej osi) krzywej jawnej, biegunowej lub parametrycznej w podanym przedziale, z pokazanymi krokami.

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.