Approach: To find the area bounded by the curve y^2 = x^3 and the line y = 2x, we need to determine the points of intersection between the curve and the line. Then, we can integrate the difference between the two functions over the interval of intersection to find the area.

Step 1: Finding Points of Intersection:
- Set y^2 = x^3 and y = 2x equal to each other:
x^3 = (2x)^2
x^3 = 4x^2
- Rearrange the equation and factor out x:
x^3 - 4x^2 = 0
x^2(x - 4) = 0
- Solve for x:
x = 0 or x = 4
- Substituting these values back into y = 2x, we get the corresponding y-values:
For x = 0, y = 2(0) = 0
For x = 4, y = 2(4) = 8
- Therefore, the curve y^2 = x^3 intersects the line y = 2x at the points (0, 0) and (4, 8).

Step 2: Calculating Area:
- To find the area bounded by the curve and the line, we integrate the difference between the two functions over the interval of intersection.
- Since the curve lies above the line, the integral is given by:
Area = ∫(2x - √(x^3)) dx from x = 0 to x = 4
- Simplify the integral:
Area = ∫(2x - x^(3/2)) dx from x = 0 to x = 4
- Integrate each term separately:
Area = (x^2 - (2/5)x^(5/2)) evaluated from x = 0 to x = 4
= [(4^2 - (2/5)4^(5/2))] - [(0^2 - (2/5)0^(5/2))]
= (16 - (2/5)4^2) - (0 - 0)
= (16 - 2(4^2))/5
= (16 - 2(16))/5
= (16 - 32)/5
= -16/5

Step 3: Final Answer:
- The area bounded by the curve y^2 = x^3 and the line y = 2x is -16/5.
- Therefore, the correct answer is option B) 16/5.