Evaluate the following:
`int_0^pi cos x dx`

Answer

To evaluate the integral \( \int_0^{\pi} \cos x \, dx \), we will follow these steps:

### Step 1: Identify the Integral
We need to evaluate the definite integral of the function \( \cos x \) from 0 to \( \pi \).

### Step 2: Find the Antiderivative
The antiderivative of \( \cos x \) is \( \sin x \). Therefore, we can write:
\[ \int \cos x \, dx = \sin x + C \]
where \( C \) is the constant of integration.

### Step 3: Evaluate the Definite Integral
Now we will evaluate the definite integral from 0 to \( \pi \):
\[ \int_0^{\pi} \cos x \, dx = \left[ \sin x \right]_0^{\pi} \]

### Step 4: Substitute the Limits
Now we substitute the upper and lower limits into the antiderivative:
\[ = \sin(\pi) - \sin(0) \]

### Step 5: Calculate the Values
We know that:
\[ \sin(\pi) = 0 \quad \text{and} \quad \sin(0) = 0 \]
Thus, we have:
\[ = 0 - 0 = 0 \]

### Final Answer
Therefore, the value of the integral \( \int_0^{\pi} \cos x \, dx \) is:
\[ \boxed{0} \]