Question 1084064
Integrate the function from the left zero to the right zero or from {{{x=0}}} to the right zero and double it (using symmetry).
To find the zeros,
{{{x^2-8=0}}}
{{{(x-sqrt(8))(x+sqrt(8))=0}}}
{{{x=2sqrt(2)}}}
{{{x=-2sqrt(2)}}}
So,
{{{A=int(f(x),dx,x=-2sqrt(2),x=2sqrt(2))}}}
{{{A=int((8-x^2),dx,x=-2sqrt(2),x=2sqrt(2))}}}
{{{A=8x-x^3/3+C}}}
{{{A=8sqrt(8)-(sqrt(8)^3)/3+8sqrt(8)-(sqrt(8)^3)/3}}}
{{{A=(64/3)sqrt(2)}}}