The Big Ideas of Calculus I
- Author:
- Prof. Caine
- Topic:
- Calculus
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 at , the rate of change of at .
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 is , the limit of the (Right) Riemann sums. It measures the difference in areas under/over the graph of over .
Fundamental Theorem of Calculus
If is continuous on then:
1) is an anti-derivative of on , i.e., on
2) If is any anti-derivative of on then