Area Mania #2

Since the graph is symmetric, then we only have to consider the area on the right side of the graph. The green area is the enclosed area between the parabolic curve and x axis minus the area between the line curve and x axis (bottom triangle).

The enclosed area between the parabolic curve and x axis is $\int_{0}^{2}\:(8 - x^2)\:dx = \frac{40}{3}$ and the area between the line curve and x axis (bottom triangle) is $\frac{1}{2}\times 4\times 2 = 4$ Thus, the green area in the right side is $\frac{40}{3} - 4 = \frac{28}{3}$ .

Then the total area is $2\times \frac{28}{3} = \frac{56}{3}$ . Hence, $A+B = 59$ .