Question

Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.

Answer 1

The given equation of the curve is y = sin x.

The required area can found by integrating y w.r.t x within the proper limits.

\[\therefore \text{Area} = \int_{x_1}^{x_2} \text{ y }dx = \int_0^\pi \sin \text{ x } dx\]

\[ = \left[ - \cos x \right]_0^\pi \]

\[ = - \cos \pi - \left( - \cos 0 \right)\]

= 1 + 1 = 2 sq. unit