There was a question here about how one can justify that integration does indeed give the area under a curve. Specifically, the OP brought up this image. The OP was troubled that even though Riemann sums intuitively "should" give the area, staircase approximation like in that image "should" give the length, so they doubted their intuition.

I found a few questions that used that image, but none of them were the one I wanted, which was specifically about Riemann integration. I don't think the question title even mentioned pi = 4, it was framed as a question about integration.

These aren't it:

  • $\begingroup$ This question would be a lot better if you gave a list of all the questions you found and ruled out... $\endgroup$ Feb 23, 2014 at 15:50
  • $\begingroup$ Is it this: math.stackexchange.com/q/43118/264 ? $\endgroup$ Feb 23, 2014 at 15:52
  • $\begingroup$ @ZevChonoles No, and I've included a list as you suggested. $\endgroup$
    – Jack M
    Feb 23, 2014 at 15:58
  • $\begingroup$ Just out of curiosity, why did you want to look up back at that question since it was posted 6 months ago? $\endgroup$
    – Hakim
    Apr 24, 2014 at 17:59
  • $\begingroup$ @حكيمالفيلسوفالضائع I was curious what the answers said. $\endgroup$
    – Jack M
    Apr 24, 2014 at 18:11

1 Answer 1


Putting your picture into Google Images "search by image" and restricting the search to site:math.stackexchange.com returns these four questions:

Based on further details provided in your post, you probably meant: Approximating an integral with rectangles? Legal?

  • $\begingroup$ That was the first trick I tried, but I didn't find that last one, which is indeed the one I wanted. Thanks. $\endgroup$
    – Jack M
    Feb 23, 2014 at 16:42

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