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Area Under the Curves question

2020 · 9 Jan · Shift 2 · Q32
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  5. /2020 · 9 Jan · Shift 2 · Q32

Area Under the Curves question

2020 · 9 Jan · Shift 2 · Q32

JEE MainMathematicsArea Under the CurvesMCQ+4 / −1
Given : f(x)={x     ,0≤x<1212    ,x=121−x   ,12<x≤1f(x) = \left\{ {\begin{matrix} {x\,\,\,\,\,,} & {0 \le x \lt {1 \over 2}} \\ {{1 \over 2}\,\,\,\,,} & {x = {1 \over 2}} \\ {1 - x\,\,\,,} & {{1 \over 2} \lt x \le 1} \\ \end{matrix} } \right.f(x)=⎩⎨⎧​x,21​,1−x,​0≤x<21​x=21​21​<x≤1​ and g(x)=(x−12)2,x∈Rg(x) = \left( {x - {1 \over 2}} \right)^2,x \in Rg(x)=(x−21​)2,x∈R Then the area (in sq. units) of the region bounded by the curves, y = ƒ(x) and y = g(x) between the lines, 2x = 1 and 2x =3\sqrt 33​, is :
  1. A
    12+34{1 \over 2} + {{\sqrt 3 } \over 4}21​+43​​
  2. B
    12−34{1 \over 2} - {{\sqrt 3 } \over 4}21​−43​​
  3. C
    13+34{1 \over 3} + {{\sqrt 3 } \over 4}31​+43​​
  4. D
    34−13{{\sqrt 3 } \over 4} - {1 \over 3}43​​−31​
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