Question

Find the area between the graph of f(x)= 8-2x^2 and the x-axis over the interval [-2,2].

Answer 1

\[-2\int_{-2}^{2}x^2dx+8\int_{-2}^{2}dx\]

Answer 2

is it 64/3 then?

Answer 3

you would take the integral of f(x)=8-3x^2:
\[\int\limits\limits_{-2}^{2} 8dx - 2\int\limits\limits_{-2}^{2}x^2dx=[8x-(2/3)x^3]\]\[[8(2)-(2/3)(2)^3]-[8(-2)-(2/3)(-2)^3]=64/3\]