## Calculus with Applications (10th Edition)

$$1$$
\eqalign{ & \int_0^{\pi /2} {\cos x} dx \cr & {\text{integrate by using the basic integration rule }}\int {\cos x} dx = \sin x + C\,\,\,\left( {{\text{page 692}}} \right) \cr & then \cr & = \left( {\sin x} \right)_0^{\pi /2} \cr & {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 388}}} \right) \cr & = \sin \left( {\frac{\pi }{2}} \right) - \sin \left( 0 \right) \cr & {\text{simplifying}} \cr & = 1 - 0 \cr & = 1 \cr}