Respuesta :

apologiabiology
the area between 2 curves, f(x) and g(x) when f(x) is above g(x) and they intersect at a and b and around x axis is
[tex]A=\pi \int\limits^a_b {f(x)^2-g(x)^2} \, dx [/tex]

alrighty, find where they intersect
x=x^2 at x=0 and x=1

and x^2 is above so

[tex]A=\pi \int\limits^1_0 {(x^2)^2-(x)^2} \, dx [/tex]
[tex]A=\pi \int\limits^1_0 {x^4-x^2} \, dx [/tex]
[tex]A=\pi[\frac{x^5}{5}-\frac{x^3}{3}]\limits^1_0[/tex]
[tex]A=\pi((\frac{1^5}{5}-\frac{1^3}{3})-(\frac{0^5}{5}-\frac{0^3}{3}))[/tex]
[tex]A=\pi((\frac{1}{5}-\frac{1}{3})-0)[/tex]
[tex]A=\pi(\frac{3}{15}-\frac{5}{15})[/tex]
[tex]A=\pi(\frac{-2}{15})[/tex]
[tex]A=\frac{-2\pi}{15}[/tex]

the area is [tex]\frac{-2\pi}{15}[/tex]

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