Question

Find the area enclosed between the X-axis and the curve y = sin x for values of x between 0 to 2π

Answer 1

Let A be the required area.

Consider the equation y = sin x.

A₁ = `int_0^"a" sin x  "d"x`

= `[- cos x]_0^pi`

= – (cos π – cos 0)

= – (–1 – 1)

= 2

A₂ = `int_pi^(2pi)sinx  "d"x`

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

= –[1 – (– 1)]

= – 2

∴ A = A₁ + |A₂|

= 2 + |(– 2)|

= 4 sq.units