Integration by Riemann Sums

The integral of a function can be defined as the limit (in a certain precise sense) of the sums of the areas of rectangles touching the graph of the function. Suppose that a typical rectangle has the interval a,b] for its base. Then you can choose among these heights for the rectangles:

f(a) —left

f(b) —right

(max_(x∈[a,b]))f(x) —max

(min_(x∈[a,b]))f(x) —min

((f(a)+f(b))/2)—mean

THINGS TO TRY

MouseOver

RELATED LINKS

Contributed by: Jiwon Hwang

© Wolfram Demonstrations Project & Contributors   |   Terms of Use