Thread: 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.

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:



which may be summed using the given:



Now hopefully evaluating this limit will give the required answer.

RonL