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NDA2022MathematicsArea Under CurvesActual

What is the area included in the first quadrant between the curves y=x and y=x^3 ?

Options

  1. A1 8 square unit
  2. B1 4 square unit
  3. C1 2 square unit
  4. D1 square unit

Correct answer

B. 1 4 square unit

Step-by-step solution

y=x ...(i) y=x^3 ..(ii) Solving equations (i) and (ii) we get Required area = ₀^1 x d x- ₀^1 x^3 d x= [ x^2 2 ]₀^1- [ x^4 4 ]₀^1= 1 2 - 1 4 = 1 4

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