If `I=int_(-2)^(2) dx`, then I equals

Options

A. 6
B. 8
C. 4
D. 21

Answer

To solve the integral \( I = \int_{-2}^{2} dx \), we will follow these steps:

### Step 1: Understand the Integral
The integral \( \int dx \) represents the area under the curve of the function \( f(x) = 1 \) from \( x = -2 \) to \( x = 2 \).

### Step 2: Perform the Integration
The integral of \( dx \) is simply \( x \). Therefore, we have:
\[ I = \int_{-2}^{2} dx = x \bigg|_{-2}^{2} \]

### Step 3: Apply the Limits
Now we will evaluate the integral by substituting the upper and lower limits:
\[ I = x \bigg|_{-2}^{2} = 2 - (-2) \]

### Step 4: Simplify the Expression
Now, simplify the expression:
\[ I = 2 + 2 = 4 \]

### Conclusion
Thus, the value of the integral \( I \) is:
\[ I = 4 \]

### Final Answer
The final answer is \( I = 4 \).

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