“G. F. B. Riemann: no gimmicks” To find the whole area under the curve, under the curve, under the curve To find the whole area under the curve, under the curve, under the curve Interval: A to B. f of x, stay with me: f of x, f of x, f of x, f of x, f of x, f of x, f of x…. I’ve a curve that’s all angles, I’m using rectangles, To find the area so? I use slices, 1 to n. Well if you want slices this is what I’ll tell ya, Each little width is B minus A over n-ah, ‘Cause width is changing-on-the x its delta - X, And height: f of x sub i from the middle, or the right or left cause you’re evaluating, from the i of the slice that you are calculating. A! The Area’s from mul-ti-plication, of the width an the height gimme some adulation. I know that you got Sigma Notation, When your slices add in a big summation! So the BCE, won’t disagree, And let me decree Archimedes. He had the same idea in ancient Greece. But it feels exhausting without Rie- mann, Hanover kid summing the bits, And more cunning and witz, than Brechtian skitz. And get on it, it’s all working out, you don’t shun it, I just set up my summation, time to sum it! And this looks like a job for Rie- mann, add it up from A to B and The more slices that you see Can increase your accuracy. And this looks like a job for Rie- mann, INTEGRAL from A to B and Sliced to infinity, for your per-fect accuracy. |