Question

Compute the area of one of the curvilinear triangles bounded by the x-axis and the curves $y=\sin x$ and $y=\cos x$.

Answer 1

area of the curvilinear triangle is the shaded region under the curve

area$={\int }_0\pi /4sinx+{\int }_{\pi /4}\pi /2cosx$

$[-cosx{]}_0^{\pi /4}+[sinx{]}_{\pi /2}^{\pi /4}$

$\frac{-1}{\sqrt{2}}+1+\frac{1}{\sqrt{2}}+1$

$=2$