SOLUTION: Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. Sketch the graph and the rectangles. Is your estimate a

Algebra ->  Test -> SOLUTION: Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. Sketch the graph and the rectangles. Is your estimate a      Log On


   

Question 1157691: Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using four approximating rectangles and right endpoints. Sketch the graph and the rectangles. Is your estimate an underestimate or an overestimate?
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Each rectangle is 1/4 wide; the values at the right endpoints are
1/(5/4) = 4/5
1/(6/4) = 2/3
1/(7/4) = 4/7
1/(8/4) = 1/2

estimated area = %281%2F4%29%284%2F5%2B2%2F3%2B4%2F7%2B1%2F2%29+=+533%2F840 = 0.6345238 to 7 decimal places.

The function is decreasing on the given interval; using right endpoints will result in an underestimate of the area.

That is easily confirmed, since the area under the curve 1/x from 1 to 2 is ln(2) = 0.6931472