Area between curve and straight line with parameter

Question

If $ f(x) = x^2 $ and $ g(x)=a ~, a \in \mathbb{R}, ~ a > 0 $, find the area between the parabola and the line that equals $4/3 $.

I know the integral is $$ A = 2\int_0^{\sqrt{a}} (a - x^2)dx = \dfrac{4} {3} \rightarrow a=1 $$

The thing is, according to my workbook, the answer is $ a = (4)^{1/3} $

I just dont see why the answer is that, even though I see that when $a=1$ the given area is not satisficied.

Thanks is advance.

Answer 1

It turned out to be that my workbook was wrong. The correct answer was $ a = 1 $, as I guessed in the first place. Sorry for the inconvenience.