Q.331. Area enclosed between two curves.

Question 331.
Find the exact area enclosed by the curve y = sinx and the line y = 1/2 for 0 < x < 2π.

 Answer 331.
Solving y = sinx with y = 1/2
=> x = π/6 and 5π/6

Required area
= ∫ (x=π/6 to 5π/6) (sinx - 1/2) dx
= [- cosx - x/2] ... (x=π/6 to 5π/6)
= [- cos(5π/6) - 5π/12] - [- cos(π/6) - π/12]
= (√3/2 - 5π/12) - (- √3/2 - π/12)
= √3 - π/3.

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