The Big Ideas of Calculus I

The derivative of a function F at 2 is the limit of the difference quotient for F at 2, written

, It measures the slope of the graph of

, the rate of change of

If we divide the interval

into

equal sub-intervals

of size

then

is called the (Right) Riemann sum for the function

over

The integral of

over

, the limit of the (Right) Riemann sums. It measures the difference in areas under/over the graph of

over

Fundamental Theorem of Calculus

is continuous on

then: 1)

is an anti-derivative of

, i.e.,

2) If

is any anti-derivative of

then