Question

Express the limit as a definite integral:

Answer 1

\[\lim_{n \rightarrow \infty} \sum_{i=1}^{n} [\cos( \frac{ \pi i }{ n })\frac{ \pi }{ n}]\]

Answer 2

lim ∑ cos[xᵢ]/[xᵢ] Δx
n→∞

Note that f(xᵢ) = cos[xᵢ]/[xᵢ]

[π, 2π] are your limits of integration

lim ∑ f(xᵢ) Δx is the Rienman expression of the ∫ f(x)dx
n→∞

So the definite integral is

2π
∫ cos[x]/[x] dx
π

Yin

Answer 3

is this a good answer:

Answer 4

integral of cos(x) from 0 to pi?

Answer 5

why did you divide by x?