### Riemann Sums

*(sung to the tune of Jingle Bells*)

Riemann Sums, Riemann Sums

Counting Areas

Of rectangles whose widths get small

We need to count them all

Riemann Sums, Riemann Sums

Counting Areas

Of rectangles whose widths get small

We need to count them all.

We learn to integrate

It's really lots of fun.

It's easier to find

Than those old Riemann Sums

We learn to sub a *u*

When things get sort of hard

But most of all we tabulate

When we get sick of parts.

[repeat the refrain]

### Derivatives, Derivatives

*(sung to the tune of O Christmas Tree)*

Derivatives, derivatives

They help us find the rate of change.

Derivatives, derivatives

They're not that hard, they're in our range.

The product rule is so much fun

It's one prime two plus two prime one

Derivatives, derivatives

They help us find the rate of change.

### Calculus Class

*(sung to the tune of Silent Night)*

Calculus class, calculus class

Teacher's cruel

Hate the Chain Rule

Find the prime of *f* of *g*

It's supposed to fill us with glee

Times *dx* of the outside

By *dx* of the inside.