Evaluate the following integrals as limit of sum: `int_0^(pi//2)cosx\ dx`

Explanation

To evaluate the integral \( \int_0^{\frac{\pi}{2}} \cos x \, dx \) as a limit of sums, we can follow these steps:

### Step 1: Set Up the Integral as a Limit of Sums
We start by expressing the integral in terms of a limit of sums. We can write:

\[ \int_a^b f(x) \, dx = \lim_{n \to \infty} \sum_{i=0}^{n-1} f(x_i) \Delta x \]
...