Question

The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is
(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq. units

Answer 1

(a) 2 sq. units



The required area ABC,
$$\begin{gathered} A={\int }_0^{\mathrm{\pi }}y\mathit{d}x \\ ={\int }_0^{\mathrm{\pi }}\sin \left(x\right)\mathit{d}x \\ ={\left[-\cos \left(x\right)\right]}_0^{\mathrm{\pi }} \\ =-\cos \left(\mathrm{\pi }\right)+\cos \left(0\right) \\ =1+1 \\ =2\mathrm{square}\mathrm{units} \end{gathered}$$