Find the riemann sum for f(x) = sin x over the interval [0, 2π], where x0 = 0, x1 = π/4, x2 = π/3, x3 = π, and x4 = 2π, and where c1 = π/6, c2 = π/3, c3 = 2π/3, and c4 = 3π/2.
I don't know for certain, but it looks like each is supposed to be the representative value of over each subinterval , so that the Riemann sum is given by
where
The sum is then
Compare to the exact value of the corresponding definite integral,
Aclassmate thinks that solving a system by graphing gives an exact answer when the lines appear to cross at a grid point, but only an approximate answer when they don't. explain why this isn't true.