JEE Main Mathematics Question (2026) — Solution

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 = _ 0 ^ 7 (-x - (x^2 - 8x)) dx A = _ 0 ^ 7 (7x - x^2) dx Evaluating the integral: A = [ 7x^2 2 - x^3 3 ]_ 0 ^ 7 A = 7(49) 2 - 343 3 A = 343 2 - 343 3 A = 343 ( 1 2 - 1 3 ) A = 343 6 Answer: 343 6