# 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 y^{2} = kx.

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## Example 5 | Plane Areas in Rectangular Coordinates

**Example 5**

Find the area between the curves 2*x*^{2} + 4*x* + *y* = 0 and *y* = 2*x*.

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## 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.

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## Example 3 | Plane Areas in Rectangular Coordinates

**Example 3**

Find the area bounded by the curve *x* = *y*^{2} + 2*y* and the line *x* = 3.

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## Example 1 | Plane Areas in Rectangular Coordinates

**Example 1**

Find the area bounded by the curve *y* = 9 - *x*^{2} and the *x*-axis.

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