if the integral from 0 to 4 of f(x) = -1
then what is the integral from -2 to 0 of x[f(x^2)]?
The Attempt at a Solution
my first instinct is that this is an even/odd definition of an integral problem. the x squared in the function makes it even, which means its symmetrical over the y-axis and thus you can double the area.
however, the x which is being multiplied by f(x^2) is confusing me as is the fact that 0 to 4 isn't the same as -2 to 2 (the symmetrical part).
can someone help me out? thanks.