Draw the rough sketch of the curve y=( x/pi  + 2sin²x)and find the area
between the x axis, the curve and the ordinates

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}}{\mathrm{\pi }}+2{\sin }^2\mathrm{x} \\ \mathrm{As} {\sin }^2\mathrm{x} \mathrm{range} \mathrm{from} 0 \mathrm{to} 1, \mathrm{and} \mathrm{is} 0 \mathrm{at} \mathrm{integral} \mathrm{multiple} \mathrm{of} \mathrm{\pi }, \mathrm{hence} \\ \mathrm{we} \mathrm{will} \mathrm{get} \mathrm{minima} \mathrm{at} \mathrm{integral} \mathrm{multiple} \mathrm{of} \mathrm{\pi }, \mathrm{and} \mathrm{maxima} \mathrm{at} \mathrm{integral} \mathrm{multiple} \\ \mathrm{of} \frac{\mathrm{\pi }}{2} \left[\mathrm{As} {\sin }^2\left\{\frac{\left(2\mathrm{n}+1\right)\mathrm{\pi }}{2}\right\}=1\right] \\ \mathrm{Hence} \mathrm{we} \mathrm{have} \end{gathered}$$$$\begin{gathered} \mathrm{Second} \mathrm{part} \mathrm{of} \mathrm{your} \mathrm{question} \mathrm{is} \mathrm{incomplete} \mathrm{as} \mathrm{you} \mathrm{haven}\text{'}\mathrm{t} \mathrm{mentioned} \mathrm{the} \\ \mathrm{ordinates}. \mathrm{Please} \mathrm{recheck} \mathrm{your} \mathrm{question}. \end{gathered}$$





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