Problema de curvas calculo integral

Graficado con winplot:

El área se calcula con laintegral:

$$\begin{align}&\int_a^b2 \pi·f(x)·\sqrt{1+[f(x)']^2} dx=\\&\\&2 \int_0^12\pi·\sqrt{4-x^2}·\sqrt{1+ \Big [\frac{-2x}{2 \sqrt{4-x^2}} \Big]^2}=\\&\\&4\pi \int_0^1 \sqrt{4-x^2} ·\sqrt{1+\frac{x^2}{4-x^2}} dx=\\&\\&4\pi \int_0^1 \sqrt {4-x^2}·\sqrt {\frac{4-x^2+x^2}{4-x^2}}dx=\\&\\&4\pi \int_0^1 \sqrt{4-x^2}·\sqrt {\frac{4}{4-x^2}}dx= 4 \pi \int_0^1 2dx= 4 \ \pi \Big[2x \Big]_0^1= \\&\\&\\&8 \pi  \ \ u^2=25.1327...\end{align}$$

Saludos

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