∫ 0 π f ( x ) d x where f ( x ) = { s i n ( x ) 0 ≤ x < π 2 c o s ( x ) π 2 ≤ x ≤ π {\displaystyle \int \limits _{0}^{\pi }f(x)dx\quad {\text{where}}\;f(x)={\begin{cases}sin(x)&0\leq x<{\frac {\pi }{2}}\\cos(x)&{\frac {\pi }{2}}\leq x\leq \pi \end{cases}}}
