[tex]\large\underline{\sf{Solution-}}[/tex]

Area bounded by curve y = cosx with x - axis, where x varies from 0 to [tex]\pi[/tex] is given by

[tex]\sf \: = \: 2\displaystyle\int_{0}^{ \frac{\pi}{2} }\sf cosx \: dx \\ \\ [/tex]

[tex]\sf \: = \: 2 \: \bigg(sinx \bigg)_{0}^{ \frac{\pi}{2} } \\ \\ [/tex]

[tex]\sf \: = \: 2\bigg(sin\dfrac{\pi}{2} - sin0 \bigg) \\ \\ [/tex]

[tex]\sf \: = \: 2\bigg(1 - 0 \bigg) \\ \\ [/tex]

[tex]\sf \: = \: 2 \: square \: units \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf f(x) & \bf \displaystyle \int \rm \:f(x) \: dx\\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf kx + c \\ \\ \sf sinx & \sf - \: cosx+ c \\ \\ \sf cosx & \sf \: sinx + c\\ \\ \sf {sec}^{2} x & \sf tanx + c\\ \\ \sf {cosec}^{2}x & \sf - cotx+ c \\ \\ \sf secx \: tanx & \sf secx + c\\ \\ \sf cosecx \: cotx& \sf - \: cosecx + c\\ \\ \sf tanx & \sf logsecx + c\\ \\ \sf \dfrac{1}{x} & \sf logx+ c\\ \\ \sf {e}^{x} & \sf {e}^{x} + c\end{array}} \\ \end{gathered}\end{gathered}[/tex]