Very Tricky Integration Question.

[worldly flare]

Someone do it or just help me please... I need to get the value of k to begin with but im not too sure how. Discriminant ? make f(x) = g(x) and solve for the points of intersection? if get the value of k i can start to try and solve for areas A & B. I can differentiate g(x) and solve for its minimum and then integrate those bounds of 0 and whatever that value is. Id do those bounds for f(x) - those bounds for g(x) to give me area A i think...
very new integrating below the x axis sm1 help i beggg

[lilac knoll]

Hm, alright, let's see. We have:
-x^2 + 2 = x^3 - x^2 - kx + 2
x^3 - kx = 0
x(x^2 - k) = 0
The solutions are x = 0 and x = ±√(k). So, by the statement of the problem, we have:
∫((x^3 - kx)dx, -√(k), 0) = ∫((kx - x^3)dx, 0, √(k))
Calculate the integrals and show that they are equal. Or show it without calculating them completely, if you can.