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

Answer 1

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