Question

Solve the following :

Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π

Answer 1

The curve y = sin x intersects the X-axis at x = 0 and x = π between x = 0 and x = π.

Two bounded regions A₁ and A₂ are obtained. Both the regions have equal areas.
∴ required area = A₁ + A₂ = 2A₁

= `2 int_0^(pi/2) y*dx,  "where"  y = sin x`

= `2int_0^(pi/2) sinx*dx`

= `2[- cos x]_0^(pi/2)`

= `2[- cos  pi/2  cos 0]`

= 2(– 0 + 1)
= 2 sq units.