WOLFRAM|DEMONSTRATIONS PROJECT

Riemann Sums

​
number of rectangles
10
height
left
midpoint
right
function
x - 1
2
x
- 1
3
x
- 1
log( x + 1 )
 1 - x
2
)\),
 x - 2 
cos( x )
x-1
The area under a curve can be approximated by a Riemann sum. The definite integral is the limit of that area as the width of the largest rectangle tends to zero. Observe that as the number of rectangles is increased, the estimated area approaches the actual area.