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KCET2024MathematicsArea Under Curves

The area of the region bounded by the line y=x and the curve y=x^3 is

Options

  1. A0.2 sq unit
  2. B0.3 sq unit
  3. C0.4 sq unit
  4. D0.5 sq unit

Correct answer

D. 0.5 sq unit

Step-by-step solution

y=x and y=x The curve intersect at x=-1, y_i=-1 ; x=0, y=0 and x=1, y=1 . Therefore, area =- _ -1 ^0 (x^3-x ) d x+ ₀^1 (x-x^3 ) d x=- [ x^4 4 - x^2 2 ]_ -1 ^0+ [ x^2 2 - x^4 4 ]₀^1=- ( 1 4 - 1 2 )+ ( 1 2 - 1 4 )=- 1 2 +1= 1 2 =0.5 sq. units

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