Express the limit as a definite integral on the given integral, [5pi,3pi].
limit notation: cos(xi)/xi
To express the limit as a definite integral, we can use the definition of the limit as a definite integral. The integral of a function f(x) over an interval [a, b] is defined as:
∫[a,b] f(x) dx
Now, let's apply this definition to the given limit: lim (xi→0) cos(xi)/xi.
To express this limit as a definite integral, we can rewrite it as:
∫[a,b] f(x) dx = ∫[a,b] cos(x)/x dx
Where a = 5π and b = 3π.
Therefore, the limit lim (xi→0) cos(xi)/xi can be expressed as the definite integral:
∫[5π,3π] cos(x)/x dx