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BITSAT2022MathematicsArea Under CurvesActual

The area enclosed by the curves y= x+ x and y=| x- x| over the interval [0, 2 ] is

Options

  1. A4( 2 -1)
  2. B2 2 ( 2 -1)
  3. C2( 2 +1)
  4. D2 2 ( 2 +1)

Correct answer

B. 2 2 ( 2 -1)

Step-by-step solution

Given, y= x+ x, x [0, / 2] d y d x = x- x aligned y & =| x- x| & = [ array cc x- x & x [0, / 4] x- x & x [ / 4, / 2] array ] aligned Required area aligned &= ₀^ / 4 |( x+ x)-( x- x)| d x+ _ / 4 ^ / 2 |2 x| d x aligned = ₀^ / 4 |2 x| d x+ _ / 4 ^ / 2 |2 x| d x=2(- x)₀^ / 4 +2( x)_ / 4 ^ / 2 =2 [- 1 2 +1+1- 1 2 ] aligned = & 2 (2- 2 2 ) = & 2(2- 2 ) = & 4-2 2 = & 2 2 ( 2 -1) aligned

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