jee-main 2020 Q67

jee-main · India · session1_09jan_shift2 Areas Between Curves Compute Area Directly (Numerical Answer)

Let $g ( x ) = \left( x - \frac { 1 } { 2 } \right) ^ { 2 } , x \in R$. Then, the area (in sq. units) of the region bounded by the curves, $y = f ( x )$ and $y = g ( x )$ between the lines $2 x = 1$ and $2 x = \sqrt { 3 }$, is:
(1) $\frac { 1 } { 3 } + \frac { \sqrt { 3 } } { 4 }$
(2) $\frac { \sqrt { 3 } } { 4 } - \frac { 1 } { 3 }$
(3) $\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 4 }$
(4) $\frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 4 }$

Let $g ( x ) = \left( x - \frac { 1 } { 2 } \right) ^ { 2 } , x \in R$. Then, the area (in sq. units) of the region bounded by the curves, $y = f ( x )$ and $y = g ( x )$ between the lines $2 x = 1$ and $2 x = \sqrt { 3 }$, is:\\
(1) $\frac { 1 } { 3 } + \frac { \sqrt { 3 } } { 4 }$\\
(2) $\frac { \sqrt { 3 } } { 4 } - \frac { 1 } { 3 }$\\
(3) $\frac { 1 } { 2 } - \frac { \sqrt { 3 } } { 4 }$\\
(4) $\frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 4 }$

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