parabolic segment

Problem 705
Determine the centroid of the shaded area shown in Fig. P-705, which is bounded by the x-axis, the line x = a and the parabola y² = kx.
 

Example 5
Find the area between the curves 2x² + 4x + y = 0 and y = 2x.
 

Example 2
Find the volume generated when the area in Example 1 will revolve about the y-axis.
 

Example 3
Find the area bounded by the curve x = y² + 2y and the line x = 3.
 

Example 1
Find the area bounded by the curve y = 9 - x² and the x-axis.