[Verse 1] There's a function dancing on the number line tonight Derivative swoops in, cuts it sharp and precise Tears apart the curve at every single point Instantaneous slopes where the tangents anoint But integration waits in shadows, patient and wide Collecting scattered pieces, bringing them inside [Chorus] Local meets global, two faces of one truth Derivative divides, integral's the proof F prime equals f, the bridge we thought we'd never see Fundamental theorem sets the captives free What tears apart, builds up again Inverse operations, eternal friends [Verse 2] Define our bridge as F of x equals integral a to x The accumulation function holds the paradox Each tiny strip of area beneath the dancing curve Adds up to something magical that calculus will serve Take the limit as h approaches zero from the right Watch the local and the global reunite [Chorus] Local meets global, two faces of one truth Derivative divides, integral's the proof F prime equals f, the bridge we thought we'd never see Fundamental theorem sets the captives free What tears apart, builds up again Inverse operations, eternal friends [Bridge] Stokes will echo this refrain Green and Gauss sing the same Boundary equals interior's call Local information conquers all De Rham cohomology knows What the prototype bestows [Verse 3] Continuous functions let the limits play With Riemann sums that never stray The antiderivative was hiding in plain sight Disguised as accumulated area taking flight From topology to physics, this pattern repeats The local-global marriage that makes math complete [Chorus] Local meets global, two faces of one truth Derivative divides, integral's the proof F prime equals f, the bridge we thought we'd never see Fundamental theorem sets the captives free What tears apart, builds up again Inverse operations, eternal friends [Outro] Two sides of one coin spinning through the air Calculus revealed the secret hiding there
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