Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four rectangles and left endpoints. Sketch the graph of f and the rectangles.

Solution:

Given f(x) = 1/x from x = 1 to x = 2

To find area, we need to find integral of f(x)

∫f(x) = ∫\(_1^2\)1/x dx

=[ log(x) + c]\(_{x =1}^2\)

= log(2) - log(1) + c

= log2 + c

Therefore, the area is log2 + c

Estimate the area under the graph of f(x) = 1/x from x=1 to x = 2 using four rectangles and left endpoints. Sketch the graph of f and the rectangles.

Summary:

The area under the curve f(x) = 1/x is log2 units.