Nov 25, 2014
We talked about how integrals will tell you the “area under a curve.” Look up above where we drew a trapezoid to find the area under the curve. A little bit of the trapezoid is actually over the curve though, so it’s not exactly the right area. But it’s close. If we want to get closer, why not use two trapezoids? Then we can add their areas together. Great, how about four trapezoids? Even better, but still a little bit off because the top of a trapezoid is straight, and the curve is curved.
With an integral it’s like you make the trapezoid width Δx infinitesimally small, in which case it becomes dx. Then you add up an infinite amount of them, so you’ve used the smallest trapezoid size possible. This gives you the true area under the curve.
