Find the area bounded by the curve y = sin x between x = 0 and $x = 2 π$ .

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Solution

The graph of y = sin x can be drawn as

Required area = Area OABO + Area BCDB

$= \int_{0}^{π} | s i n x | d x | + \int_{π}^{2 π} | s i n x | d x = \int_{0}^{π} | s i n x | d x | + \int_{π}^{2 π} | - s i n x | d x (∵ s i n x \geq 0 f o r x ϵ [0, π] a n d s i n x \leq 0 f o r x ϵ [π, 2 π]) = [- c o s x]_{0}^{n} + [c o s x]_{π}^{2 π} = - c o s π + c o s 0 + c o s 2 π - c o s π = - (- 1) + 1 + 1 - (- 1) = 4 s q u n i t$

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Similar questions

y = sin x

x = 0

x = 2 π

y = sin x

x = 0

x = 2 π

Area bounded by the curve y = sin x between x = 0 and x = 2 $π$ is

y = x + s i n x

x = 0

x = 2 π

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