NCERT Class 12 · Ch 8 Miscellaneous Exercise · Q5
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Miscellaneous Exercise Question 5
Find the area bounded by y=x|x|, the x-axis, x=−1 and x=1.
💡 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: C: 2/3 square units.
- For x<0, y=−x²; for x≥0, y=x².
- The area is ∫₋₁⁰x²dx+∫₀¹x²dx, using the absolute value of the vertical height.
- Each integral is 1/3, so the total is 2/3, option C. The signed integral of the original odd function would instead be zero.
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