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Question
Find the area of the region bounded by the curve y = sin x, the X−axis and the given lines x = − π, x = π
Solution
Let A be the required area.
Consider the equation y = sin x
∴ A = `int_(-pi)^pi y "d"x`
= `int_(-pi)^pi sin x "d"x`
= `|int_(-pi)^0 sin x "d"x| + int_0^pi sin x "d"x`
= `|[- cos x]_(-pi)^0| + [- cos x]_0^pi`
= | – [cos 0 – cos (– π)]| – (cos π – cos 0)
= | – [1 – (–1)] | – (–1 – 1)
= |– 2| + 2
= 2 + 2
= 4 sq.units
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