NCERT Class 12 · Ch 8 Miscellaneous Exercise · Q4
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Miscellaneous Exercise Question 4
Find the area bounded by y=x³, the x-axis, x=−2 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: D: 17/4 square units.
- The cubic is negative on [−2,0] and positive on [0,1].
- Area=−∫₋₂⁰x³dx+∫₀¹x³dx.
- Using the primitive x⁴/4 gives −(0−16/4)+(1/4−0)=4+1/4=17/4, option D.
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