Introduction:
To find the area of the region bounded by the circle x^2 + y^2 = 9 and the parabola y^2 = 8x, we will first identify the points of intersection between the two curves. Then, we will integrate to find the area between these points of intersection.

Identifying Points of Intersection:
To find the points of intersection, we need to solve the two equations simultaneously. Let's start by substituting y^2 = 8x into the equation of the circle:

x^2 + (8x)^2 = 9
x^2 + 64x^2 = 9
65x^2 = 9
x^2 = 9/65

Taking the square root of both sides, we get:
x = ±√(9/65)

Substituting these values of x back into the equation of the parabola, we can find the corresponding y-values.

For x = √(9/65):
y^2 = 8(√(9/65))
y^2 = 72/65
y = ±√(72/65)

For x = -√(9/65):
y^2 = 8(-√(9/65))
y^2 = -72/65 (no real solutions)

So, the points of intersection are (√(9/65), √(72/65)) and (-√(9/65), -√(72/65)).

Calculating the Area:
To calculate the area of the bounded region, we will integrate the difference between the y-values of the circle and the parabola from the lower x-value (√(9/65)) to the higher x-value (-√(9/65)).

The equation of the circle is y = √(9 - x^2), and the equation of the parabola is y = ±√(8x).

Let's integrate the difference between these equations with respect to x:

A = ∫[(-√(72/65)) to (√(72/65))] [(√(9 - x^2)) - (√(8x))] dx

Evaluating this integral will give us the area of the bounded region.

Conclusion:
By finding the points of intersection between the circle x^2 + y^2 = 9 and the parabola y^2 = 8x, and then integrating the difference between the y-values of these curves, we can calculate the area of the region bounded by them.