# Ejercicio 9.17

kill(all)$

## Apartado 1)

Eq1: x^2 = 4*y$           Eq2: y = 1/(x^2 + 3)$
solve ([Eq1, Eq2] , [x,y]);

f1(x) := x^2/4;
f2(x) := 1/(x^2 + 3);

wxplot2d([f1(x),f2(x)], [x,-1,1], [y, 0, 0.5] , [legend, "f1(x)" , "f2(x)"] , [style, [lines, 2]] ,
[gnuplot_preamble, "set size ratio 1; set grid"], [nticks, 300] )$

## Apartado 2)

Area = integrate (f2(x) , x, -1, 1) -  integrate (f1(x) , x, -1, 1) ;

%, numer ;

## Apartado 3)

g1(y) := sqrt(4*y);
g2(y) := sqrt(1/y - 3);

V1 = V1: %pi * integrate ((g1(y))^2, y, 0, 1/4) ;

V2 = V2: %pi * integrate ((g2(y))^2, y, 1/4, 1/3) ;

Volum = V1 + V2, numer;