Find by the method of integration the area of the region bounded by the parabola `y^2=8x` and its latus rectum.

Explanation

To find the area of the region bounded by the parabola \( y^2 = 8x \) and its latus rectum, we can follow these steps:

### Step 1: Identify the Latus Rectum
The given parabola is in the form \( y^2 = 4ax \), where \( 4a = 8 \). Thus, we have \( a = 2 \). The latus rectum of a parabola \( y^2 = 4ax \) is a vertical line given by \( x = a \). Therefore, for our parabola, the latus rectum is at:

\[ x = 2 \]
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