I know how to solve it by the use of integrals, but I wonder why solving it using a graph would bring incorrect result? I mean, why would it be wrong to just consider roots of these functions and solve it drawing solely on them?
Consider two functions:
$f (x) = a − x^2 $
$g(x) = x^4 − a $ For precisely which values of $a > 0$ is the area of the region bounded by the $x$-axis and the curve $y=f(x)$ bigger than the area of the region bounded by the $x$-axis and the curve $y=g(x)$?