Consider the curve y^2=4+x and chord AB joining points A(-4, 0) and B(0,2) on the curve.

start by making a sketch of the parabola and chord ...
1. Find the x- and y-coordinates of the point on the curve where the tangent line is parallel to chord AB.

set the slope of AB = derivative of the curve, solve.
2. Find the area of the region R enclosed by the curve and chord AB.

find the equation of line AB, y = mx+b
3. Find the volume of the solid generated when the region R, defined in part 2., is revolved about the x-axis.

method of washers ...