I'm having a conceptual problem with integrating a function and thought someone might enlighten me.(adsbygoogle = window.adsbygoogle || []).push({});

Say you have a simple function which is the simple slope 3/4. You take the definite integral of it an come up with 3/4 x evaluated between two values of x. Good so far.

Now, if I set the limits of integration between 0 and 4, I get a value of 3. We'll call the area, then, 3 meters squared. Good so far again.

Going further, if I set the limits of integration for high values of x with the same difference of 4 units, I still get the value of three when I plug in the limits of integration. For example, setting the limits at 400 to 396, still gives an answer of 3 square meters.

My conceptual problem is that, when I visualize this slope over 400 units of x, I see the same horizonal displacement on the graph, but I see an ever increasing vertical displacement. This leads me to believe that the area of each rectangular "slice" must be growing for higher values of x. But the maths say they are the same. I'm befuddled.

What is going on here, are the "slices" of 4 units getting thinner and thinner for higher values of x or am I missing something here?

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# Area under a function befuddlement

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