Find integrals of given functions
`{:(" "1),(" "int),(-2):} 5dx`

Options

A. 15
B. -5
C. -15
D. 5

Answer

To find the integral of the function \(5 \, dx\) from \(-2\) to \(1\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Integral**: We need to evaluate the definite integral:
\[ \int_{-2}^{1} 5 \, dx \]

2. **Recognize the Constant**: Since \(5\) is a constant, we can factor it out of the integral:
\[ = 5 \int_{-2}^{1} dx \]

3. **Evaluate the Integral of \(dx\)**: The integral of \(dx\) over the limits \(-2\) to \(1\) is simply the difference between the upper and lower limits:
\[ \int_{-2}^{1} dx = x \bigg|_{-2}^{1} = 1 - (-2) = 1 + 2 = 3 \]

4. **Multiply by the Constant**: Now, we multiply the result by the constant \(5\):
\[ = 5 \times 3 = 15 \]

5. **Final Result**: Thus, the value of the definite integral is:
\[ \int_{-2}^{1} 5 \, dx = 15 \]