NCERT Class 12 · Ch 8 Miscellaneous Exercise · Q2
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Miscellaneous Exercise Question 2
Sketch y=|x+3| and evaluate ∫₋₆⁰|x+3| dx.
💡 Concept Hints
- Sketch the region, choose a vertical or horizontal strip, and find all sign changes.
- Express its area as an integral of upper minus lower (or right minus left), splitting where necessary.
✅ Step-by-Step Solution
Final Answer: 9.
- The graph is a V with vertex (−3,0); y=−x−3 for x≤−3 and y=x+3 for x≥−3.
- Split at x=−3: I=∫₋₆⁻³(−x−3)dx+∫₋₃⁰(x+3)dx.
- The first integral [−x²/2−3x]₋₆⁻³=9/2. The second [x²/2+3x]₋₃⁰=9/2.
- Thus I=9. Geometrically these are two triangles, each base 3 and height 3.
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