Question:
\( \int_{-2}^{2} |x| dx \) is equal to
\( \int_{-2}^{2} |x| dx \) is equal to
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Always split absolute value integrals at sign change.
Updated On: May 1, 2026
- \( 0 \)
- \( 1 \)
- \( 2 \)
- \( 4 \)
- \( \frac{1}{2} \)
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The Correct Option is D
Solution and Explanation
Concept: Break absolute value integral.
Step 1: Split interval.
\[ [-2,0] \cup [0,2] \]
Step 2: Apply definition.
\[ |x| = -x \text{ for } x0 \]
Step 3: Compute integrals.
\[ \int_{-2}^{0} (-x)dx = 2 \] \[ \int_{0}^{2} xdx = 2 \]
Step 4: Add values.
\[ 2+2=4 \]
Step 5: Final result.
\[ 4 \]
Step 1: Split interval.
\[ [-2,0] \cup [0,2] \]
Step 2: Apply definition.
\[ |x| = -x \text{ for } x0 \]
Step 3: Compute integrals.
\[ \int_{-2}^{0} (-x)dx = 2 \] \[ \int_{0}^{2} xdx = 2 \]
Step 4: Add values.
\[ 2+2=4 \]
Step 5: Final result.
\[ 4 \]
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