parabolic segment

705 Centroid of parabolic segment by integration

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.

Open to the right parabola in the first quadrant


Example 5 | Plane Areas in Rectangular Coordinates

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

Example 2 | Volumes of Solids of Revolution

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