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Question
Find the area bounded by the curve y = 2cosx and the x-axis from x = 0 to x = 2π
Solution
Given equation of the curve is y = 2 cos x
∴ Area of the shaded region = `int_0^(2pi) 2 cos x "d"x`
= `int_0^(pi/2) 2 cos x "d"x + int_(pi/2)^((3pi)/2) |2 cos x|"d"x + int_((3pi)/2)^(2pi) 2 cos x "d"x`
= `2[sin x]_0^(pi/2) + |[2 sin x]_(pi/2)^((3pi)/2)| + 2[sin x]_((3pi)/2)^(2pi)`
= `2[sin pi/2 - sin 0] + |2(sin (3pi)/2 - sin pi/2)| + 2[sin 2pi - sin (3pi)/2]`
= `2(1) + |2(-1 - 1)| + 2(0 + 1)`
= 2 + 4 + 2
= 8 sq.units
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