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JEE Main20266 April 2026Evening ShiftMathematicsArea Under CurvesActual

The area of the region (x, y) : x^2 - 8x y -x is :

Options

  1. A343 6
  2. B637 6
  3. C437 6
  4. D523 6

Correct answer

A. 343 6

Step-by-step solution

The given region is bounded by the parabola y = x^2 - 8x and the line y = -x . To find the points of intersection, equate the two equations: x^2 - 8x = -x x^2 - 7x = 0 x(x - 7) = 0 The points of intersection are x = 0 and x = 7 . In the interval [0, 7] , the line y = -x lies above the parabola y = x^2 - 8x . The required area A is given by: A = ₀⁷ (-x - (x^2 - 8x)) dx A = ₀⁷ (7x - x^2) dx Evaluating the integral: A = [ 7x^2 2 - x^3 3 ]₀⁷ A = 7(49) 2 - 343 3 A = 343 2 - 343 3 A = 343 ( 1 2 - 1 3 ) A = 343 6 Answer:

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