Final answer:
The area bounded by the x-axis and the curve x^2 = 4ay, when x = a, is (a²/8).
Step-by-step explanation:
To find the area bounded by the x-axis and the curve represented by the equation x^2 = 4ay, we need to determine the limits of integration. Since the ordinate x = a, we can substitute this value into the equation to find the corresponding value of y.
Substituting x = a into x^2 = 4ay gives a^2 = 4ay. Dividing both sides by 4a, we get a/4 = y. Therefore, the curve intersects the x-axis at y = a/4.
The area bounded by the x-axis and the curve is equal to twice the area of the region above the x-axis, since the curve is symmetric about the x-axis. Using the definite integral, the area is given by:
A = 2 ∫[a/4, 0] y dx = 2 ∫[a/4, 0] (a/4) dx = 2(a/4) ∫[a/4, 0] dx = a/2 [x]∣[a/4, 0] = a/2 [(0) - (a/4)] = a²/8
Therefore, the area bounded by the x-axis and the curve x^2 = 4ay is (a²/8).