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Answer 1

$\tt The\: area \: bounded \: by \: the \: curve \: y = {sin}^{2}(\frac{x}{2})\: and\: x\:axis \\ \\ \tt The \: coordinates \: are \: x = 0 , \frac{\pi}{2} \\ \\ \tt The\: area \: of \: curve \: is \: given \: as \\ \\ \tt A = \int \limits_{0}^{\frac{\pi}{2}} {sin}^{2}(\frac{x}{2}) dx \\ \\ \tt Multiplying\:and\: dividing\:by\:2 \\ \\ \tt A = \frac{1}{2} \int \limits_{0}^{\frac{\pi}{2}} 2{sin}^{2}(\frac{x}{2})dx \\ \\ \tt A = \frac{1}{2} \int \limits_{0}^{\frac{\pi}{2}} ( 1 - cosx )dx \\ \\ \tt A = \frac{1}{2} (x - sin x) \\ \\ \tt A = \frac{1}{2} (\frac{\pi}{2} - 0 - sin\frac{\pi}{2} + sin0) \\ \\ \tt A = \frac{1}{2}( \frac{\pi}{2} - 1 ) \\ \\ \boxed{\bold{\underline{\red{\tt A = \frac{1}{2}(\frac{\pi}{2} - 1 ) \:sq.units }}}} \\ \\ \bold{\huge{\orange{\mathfrak{Shreya}}}}$

Answer 2

See the above Answer...

Option D is the correct answer