Approximating Areas

Question

(A) Estimate the area under the graph of f(x) = 7/x from x = 1 to x = 7 using 6 approximating rectangles and right endpoints.

Estimate =

B) Repeat part (A) using left endpoints

Estimate =

Answer 1

Simple, make a table of x and 7/x from x = 1 to 7. Since the width of each rectangle is Δx = 1, just add up the appropriate values. A) Sum of all but first = _____. B) Sum of all but last = _____.

[Average of the two is 14.15. Exact value is 7∫₁⁷ 1/x = 7 [ln x]₁⁷ = 7 [1.946... - 0] ≅ 13.62]