# Riemann Sum of semi-sircle

Can anyone please direct me in the right way on working out the approximate area of a semi-circle with equation y = (r^2 - x^2)^0.5, by using a Riemann Sum

dextercioby
Homework Helper
What do you know about Riemann sums (meaning their general formula for the case of simple definite integrals)...?
Chose a system of coordinates with the center at the left end of the semicircle,so that the Ox axis in its posotive part to comprise entire diameter.Therefore your equation for the curve will be slightly modified.

Daniel.

quasar987
Homework Helper
Gold Member
Here's what I suggest..

First find the domain of that function ([-3,3]). Then create an arbitrary partition of that domain. That is to say, select an arbitrary number of points in that domain and label them $\{x_0, x_1,...x_n\}$. (x0 has to be -3 and xn has to be 3). In principle, the more points you chose, the better the approximation.

Then construct and evaluate the Riemann sum

$$\Sigma_{i=1}^{n} y(t_i)(x_{i}-x_{i-1})$$

Where the ti are arbitrarily chosen points in the interval $[x_{i-1},x_{i}][/tex] dextercioby Science Advisor Homework Helper Yes,but i suggested him that all values of the partition be positive,the way you took'em half are and half are not...I think that should create some avoidable problems... Daniel. quasar987 Science Advisor Homework Helper Gold Member Really? Like what? I don't see what the difference will be, since [itex]x_{i}-x_{i-1}$ will be positive anyway.

I got a cool program on my graphing calculator that does that for me. It's handy when it comes to test. If you want it, just pm me.

dextercioby