You are going to be using the formula

First see that you are taking the integral from until that is when it intersects the x and y axes.

Now you need to find :

Notice that implies .

At the width of the line perpendicular to the x-axis is then . But this is the diameter of the circle. Thus, its radius is .

The area of this cross section (semicircle) is

(remember the 1/2 it is semi-circle )

Thus,

I think there is something wrong with your choices.