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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 at all angles, I’m using rectangles,
to find 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, add it up from A to B and
the more slices that you see
can increase your accuracy.
Little slices, make area nicest.
The smallest of sizes will be the precisest.
Infinitesima-al bits will entice us,
'till someone comes along with a vision and yells, SWITCH!
A visionary, vision of area,
to start the transformation,
Summation is changing with limits,
‘n’ is getting greater so vast that,
it’s a fact that I know that those little slices outlast,
Attempts to count them!
What a catastrophe!
Cause there can’t be enough
Time to count to infinity!
But step back.
n n n n n n n n n n.
There’s no width to measure,
truly thin, so change the letter,
d for Delta. A differential trend setter.
The new Sigma notation, slimmer is better!
And it’s the best thing,
the S thing’s suggesting.
Divesting x of the sub i, I’m stressing:
An-ti – der-i-va –tive.
When I mention integral of f x d
x. Who made sense, intense from A to B?
Ah Newton? Not him. No not Cauchy.
No! 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, 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’s INTEGRAL from A to B and
sliced to infinity,
for your per-fect accuracy.