integrals and sigma notation?

Question

how do you convert an integral into sigma notation?

for example

the integral of x(3-x)^(1/2) from 0 to 3

with four intervals

what do you do!??!?!

Answer 1

if i understand the question correctly integral is summation and sigma notation is also used for summation
sigma 0 to 1/2 x(3-x)^1/2+sigma 1/2 to 1 x(3-x)^1/2+sigma 1 to 2x(3-x)^1/2+sigma 2 to 3 x(3-x)^1/2

Answer 2

I think you are asking for a discrete sum approximation for the integral.

So, think "area under the curve" for four equal x-intervals of your function.

Calculate the areas of the four rectangles so defined, and add them.

Let f(x)=x(3-x)^(1/2)

Area under curve =~ SIGMA [ f(x) * delta x], where delta x is the length of the inteval you choose for the approximation. If you want four equal intervals between 0 and 3, delta x = 0.75.

So, substitute x= 0, .75, 1.5, 2.25 into f(x) to get the leading "height" of your rectangles, and multiply the sum of those heights by 0.75 to get the approximation of the area.

You can also do a trailing "height" approximation, using 0.75, 1.5, 2.25, and 3 as your x's.

I hope this helps.