Integrals — Class 12 Maths Solution

: Let$\int\limits_0^\pi {\left( {{{\sin }^2}\cfrac{x}{2} - {{\cos }^2}\cfrac{x}{2}} \right)dx} = - \int\limits_0^\pi {\cos x} dx$

$= - \left[ {\sin x} \right]_0^\pi = - \left( {\sin \pi - \sin 0} \right) = - \left( {0 - 0} \right) = 0$