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BITSAT2024MathematicsArea Under CurvesActual

The area enclosed by the curves y=x^3 and y= x is

Options

  1. A5 3 sq. units
  2. B5 4 sq. units
  3. C5 12 sq. unit
  4. D12 5 sq. units

Correct answer

C. 5 12 sq. unit

Step-by-step solution

Given curves are y=x^3 and y= x Both curves intersects at x=0 and x=1 Shaded region is required area aligned A & = | ₀^1 (x^3- x ) d x |= | [ x^4 4 - 2 x^ 3 / 2 3 ]₀^1 | & = | [ 1 4 - 2 3 ] | & = 5 12 sq. unit aligned

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