Since , use limits, then we should probably use a Riemann sum and calculate as n → ∞.

Interval : x = 0 to 3(i.e, b = 3 and a = 0)

Number of subintervals : n

Let f (t) be a function that is continuous on the interval a ≤ t ≤ b. Divide this interval into n equal width subintervals, each of which has a width of $\"delta$ .

Subintervals width : $\"\"$ .

For each subinterval, we have rectangle with width = $\"\"$ and height = f(x), where f(x) = x^2

Using Right Riemann sum, we get :

Area of the rectangle $\"\"$ .

Area $\"\"$

To find exact area, take limit as n → ∞.

Area $\"\"$

Area $\"\"$ .

Therefore, area of the region bounded by the curve y = x^2, the positive x - axis and the line x = 3 is 9 square units.