
Reimann sums
Consider the Riemann sum of the function f(x) = cos(2x) on the interval (0,pi/2) with
n = 3 equal size subintervals, that uses the right endpoint of each subinterval as the sample
point.
a) Write down the above sum using sigma notation; do not simplify or evaluate.
b) Evaluate the sum; simplify, but do not approximate.
Please help my teacher spent like 5 minutes on this in class and now its on our assignment.
Thanks in advance.

Re: Reimann sums
i will tel you HOW to do this, but you will have to actually DO it yourself.
we have an interval [0,π/2], and we are going to chop it up into 3 equal pieces.
this will becomes the THREE intervals [0,π/6], [π/6,π/3] and [π/3,π/2].
so our righthand endpoints are:
π/6, π/3 and π/2.
we are going to approximate the area between the curve f(x) = cos(2x) and the xaxis, by three rectangles:
the rectangles will have HEIGHT f(x_{i}), where x_{i} is one of our 3 endpoints, and each rectangle will have a BASE (width) of length (1/3)(π/2) = π/6.
so we're going to have 3 terms in our sum, each one will look like:
cos(2x_{i})(π/6). i leave it to you to put this in "sigma" notation.
the GENERAL form of a riemann sum from a to b is:
$\displaystyle \sum_{i=1}^n f(x_i^\ast)(x_{i+1}  x_i)$ where x_{1} = a, and x_{n+1} = b, and for each i, x_{i} < x_{i+1}.
often, the subintervals [x_{i},x_{i+1}] are all chosen to be the same size, while x_{i}* is allowed to be ANY point in [x_{i},x_{i+1}].
it is, however, customary to pick a surefire way of coming up with some "organized" way of picking the x_{i}* (such as left endpoint, right endpoint, midpoint, maximum value or minimum value). if f is a continuous function, and n is large enough, it won't make "too much difference" which point we pick, because all these values will be "close together".

Re: Reimann sums
You might check out this thread:
http://mathhelpforum.com/calculus/20...emannsum.html
It's almost exactly the same question  just a different function and a different interval.
 Hollywood