Question

Use the limit process to find the area of the region bounded by the graph of the function

f(x) = x + 2 and the y-axis over the interval of 0 ≤ x ≤ 2. (i.e. divide the interval into n even

sub-intervals, and find the sum of the area of rectangles, and take the limit n → ∞.) Check your

answer with the geometric formula.

Answer 1

Number of sub intervals : n

Let the f(x) be a function and is continuous on the interval a ≤ x ≤ b.

Divide this interval into n equal width subintervals, each of which has a width of   ∆x = (b - a)/n

And so on ,we then have

The Riemann sum is then

Using Right Riemann sum, we get :

Area of the rectangle

Area = 6 square units.