NCERT Class 12 · Ch 8 Miscellaneous Exercise · Q3
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Miscellaneous Exercise Question 3
Find the area bounded by y=sin x and the x-axis between x=0 and x=2π.
💡 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: 4 square units.
- sin x≥0 on [0,π] and sin x≤0 on [π,2π].
- Therefore area=∫₀^π sin x dx−∫_π^(2π) sin x dx.
- The first integral is [−cos x]₀^π=2; the second is [−cos x]_π^(2π)=−2.
- The geometric area is 2−(−2)=4.
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