Question

Approximate the area under the curve and above the x-axis using n rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle.

f(x)=3/x from x=2 to x=6; n=4

Answer 1

for x = 3,4,5,6
f(x) = 1,3/4,3/5,1/2

Now just add up all the rectangles of width 1.

Answer 2

I'm lost here. I think i'm adding wrong numbers or something else here.

Answer 3

I guess you must be. Draw a diagram, and draw 4 rectangles of width 1, from

x=2-3, 3-4, 4-5, 5-6 high enough so that the top right corner of each rectangle intersects the graph of y=3/x.

rectangle are thus

1 x 1
1 x 3/4
1 x 3/5
1 x 3/6

Approximate the area under the curve by adding up the areas of all the rectangles. That is,

1 + 3/4 + 3/5 + 1/2 = 57/20 = 2.85