NCERT Class 12 · Ch 8 Miscellaneous Exercise · Q1
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Miscellaneous Exercise Question 1
Find the area between the curve and x-axis for (i) y=x², 1≤x≤2; (ii) y=x⁴, 1≤x≤5.
💡 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: (i) 7/3; (ii) 3124/5 square units.
- Both curves are nonnegative on their stated intervals, so their integrals equal geometric areas.
- (i) ∫₁²x²dx=[x³/3]₁²=(8−1)/3=7/3.
- (ii) ∫₁⁵x⁴dx=[x⁵/5]₁⁵=(3125−1)/5=3124/5.
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