Integral of greatest integer function and its graph

[tensaiyan]

Homework Statement

Calculus problem.

How to calculate the integral of greatest function y=[1/x] ? And can someone please show me how to draw the graph of that function . Upper limit= 1,lower limit= 1/n (where n is natural number)

Please give me some hints or explanations for this kind of integral.

Relevant Equations

I already tried to answer the question but don’t know whether the answer is right or not. I attach some of my steps done below.

 

[LCKurtz]

I won't try to read a sideways picture, but here's the picture you asked for:

showing jumps at ##\frac 1 2,~ \frac 1 3,~ \frac 1 4## etc. Ignore the glitches in the vertical lines. You just need to calculate the area under the graph from ##\frac 1 n## to ##1##.

 

[tensaiyan]

I won't try to read a sideways picture, but here's the picture you asked for:
View attachment 246783
showing jumps at ##\frac 1 2,~ \frac 1 3,~ \frac 1 4## etc. Ignore the glitches in the vertical lines. You just need to calculate the area under the graph from ##\frac 1 n## to ##1##.

Thanks,it was very really helpful!