Evaluate Integral: sinπ(k/2) with k = 1 to 6

[dx/dy=?]

Question,
Evaluate:
$$\sum_{k=1}^{\ 6}\ f(xk)$$
where
$$\ xk\ = \ k/2$$
and
$$\ f(x)=sin\pi\ x$$

OK,
does this mean that that I should form a RiemannSum with;
$$sin\pi\ (k/2)* delt(k/2)= \sum_{k=1}^{\ 6}f(k/2)delt(k/2)$$

Im confused.

 

[Maxos]

I cannot see your problem, it is a trivial substitution

$$\sum_{k=1}^{\ 6}\ f(xk) = \sum_{k=1}^{\ 6}\ \sin(k\frac{\pi}{2})=1$$

 

[dx/dy=?]

Thankyou,
sometimes I get muddled when working with calculus, and often percieve things as being a lot harder than they are.

Thanks again.

 

[Maxos]

Ok, quite an usual occurrence!