Question

$\int_{-2}^{2}|x+3|\,dx =$

• A. 14
• B. 16
• C. 8
• D. 10
• E. 12

Hint:

If the function does not change sign in the interval, you can simply remove the absolute value bars.

Answer 1

Answer: (E)

Step 1: Concept
Check if the function inside the absolute value changes sign in the interval $[-2, 2]$.

Step 2: Analysis
$x+3 = 0 \implies x = -3$. Since $-3$ is outside the interval $[-2, 2]$, $|x+3| = x+3$ for the entire range.

Step 3: Calculation
$\int_{-2}^{2} (x+3) dx = [\frac{x^2}{2} + 3x]_{-2}^{2} = (\frac{4}{2} + 6) - (\frac{4}{2} - 6) = 8 - (-4) = 12$. Final Answer: (E)