# Riemann Sums

• May 12th 2008, 04:01 AM
Number Cruncher 20
Riemann Sums
Hi,

we've been asked to find the L(f,Pn) of the function f(x)= sin(x) over the interval [0,a] where 0 ˂ a ≤ 1 and the partition of the interval into n subintervals of even length and find the lim [L(f,Pn)]
n

we are also given:

n
∑ sin(ix) = [[sin(x(n+1)/2)sin(nx/2)]/sin(x/2)]
i=1

Would really appreciate the help.
• May 13th 2008, 12:59 AM
CaptainBlack
Quote:

Originally Posted by Number Cruncher 20
Hi,

we've been asked to find the L(f,Pn) of the function f(x)= sin(x) over the interval [0,a] where 0 ˂ a ≤ 1 and the partition of the interval into n subintervals of even length and find the lim [L(f,Pn)]
n

we are also given:

n
∑ sin(ix) = [[sin(x(n+1)/2)sin(nx/2)]/sin(x/2)]
i=1

Would really appreciate the help.

.

If I understand your notation correctly, in this case:

$L(f,Pn)=(a/n) \sum_{i=0}^{n-1} \sin(i(a/n))$

which may be summed using the given:

$L(f,Pn)=(a/n) \frac{\sin\left(\frac{a(n+1)}{2n}\right)\sin(\frac {a}{2})}{\sin(\frac{a}{2n})}$

Now hopefully evaluating this limit will give the required answer.

RonL