question_answer

The area bounded by the curves  y = cos x and y = sin x between the ordinates x = 0 and \[x=\frac{3\pi }{2}\] is

A) \[\left( \text{4}\sqrt{\text{2}}\text{-2} \right)\text{sq units}\]

B) \[\left( \text{4}\sqrt{\text{2}}\text{+2} \right)\text{sq units}\]

C) \[\left( \text{4}\sqrt{\text{2}}-1 \right)\text{sq units}\]

D)  \[\left( \text{4}\sqrt{\text{2}}+1 \right)\text{sq units}\]

Correct Answer: A

Solution :

Required area         \[\begin{align}   & Ca{{\left( OH \right)}_{20}}+2C{{O}_{2}}\to Ca{{\left( HC{{O}_{3}} \right)}_{2}} \\  & \text{YExcessZ} \\ \end{align}\]                                             \[\begin{align}   & Ca{{\left( HC{{O}_{3}} \right)}_{2}}\xrightarrow{Heat}CaC{{O}_{3}}+C{{O}_{2}}\uparrow +{{H}_{2}}O \\  & ZX \\ \end{align}\] \[\begin{align}   & Zn{{\left( OH \right)}_{2}}+2\overset{-}{\mathop{OH}}\,\to ZnO_{2}^{2-}+2{{H}_{2}}O \\  & \text{AcidBaseSaltWater} \\ \end{align}\]                                              \[\begin{align}   & Zn{{\left( OH \right)}_{2}}+2{{H}^{+}}\to Z{{n}^{2+}}+2{{H}_{2}}O \\  & \text{BaseAcidSaltWater} \\ \end{align}\] \[{{\left[ \text{Cu}{{\left( \text{N}{{\text{H}}_{\text{3}}} \right)}_{\text{4}}} \right]}^{\text{2+}}}\text{}{{\left[ \text{Cu}{{\left( \text{en} \right)}_{\text{2}}} \right]}^{\text{2+}}}\text{}{{\left[ \text{Cu}\left( \text{trien} \right) \right]}^{\text{2+}}}\text{.}\]