Find integrals of given functions
`int_(0)^(pi) cos x dx`

Answer

To solve the integral \( \int_{0}^{\pi} \cos x \, dx \), we can follow these steps:

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

### Step 2: Find the antiderivative
The antiderivative (or indefinite integral) 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: Apply the limits of integration
Now, we need to 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
We will substitute the upper limit \( \pi \) and the lower limit \( 0 \) into the antiderivative:
\[ = \sin(\pi) - \sin(0) \]

### Step 5: Calculate the values
We know that:
- \( \sin(\pi) = 0 \)
- \( \sin(0) = 0 \)

Thus, substituting these values gives:
\[ = 0 - 0 = 0 \]

### Final Answer
The value of the integral \( \int_{0}^{\pi} \cos x \, dx \) is \( 0 \).

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