The intercepts on the x -axis made by tangents to the curve, y = ∫ 0 x t d t , x ∈ R , which are parallel to the line y = 2 x , are equal to

Step-by-step solution

Given y = ∫ 0 x t d t If x > 0 , then y = ∫ 0 x t d t ⇒ y = x 2 2 Ff x < 0 , then y = − x 2 2 ∴   y = x 2 / 2 , x > 0 - x 2 / 2 , x < 0 Now, d y d x = x , x > 0 - x , x < 0 Slope of tangent = 2 Hence x = 2 ,   y = 2 or x = - 2 ,   y = - 2 Eq. of tangent y = 2 x - 2 or y = 2 x + 2 Hence, x - intercept = 1 or - 1 .