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KCET2024MathematicsArea Under Curves

The area of the region bounded by the line y=3 x and the curve y=x^2 sq units is

Options

  1. A10
  2. B9 / 2
  3. C9
  4. D5

Correct answer

B. 9 / 2

Step-by-step solution

We have, y=3 x and y=x^2 3 x=x^2x=3 and x=0 are the points of intersection. Now, area = ₀^3 (3 x-x^2 ) d x= . 3 x^2 2 |₀ ^3- . x^3 3 |₀ ^3=3 9 2 - 27 3 = 27 2 -9= 9 2 sq units

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