Let the curve y = y x be the solution of the differential equation, d y d x = 2 x + 1 . If the numerical value of area bounded by the curve y = y x and x -axis is 4 8 3 , then the value of y 1 is equal to ________.

Step-by-step solution

d y d x = 2 x + 1 ⇒ ∫ d y = ∫ 2 x + 1 d x ⇒ y x = x 2 + 2 x + C Area = 4 8 3 ⇒ 2 ∫ - 1 - 1 + 1 - C - x + 1 2 - C + 1 d x = 4 8 3 ⇒ 2 - x + 1 3 3 - C x + x - 1 - 1 + 1 - C = 4 8 3 ⇒ - 1 - C 3 + 3 C - 3 C 1 - C - 3 C - 3 + 3 1 - C + 3 = 2 8 ⇒ C = - 1 ⇒ f x = x 2 + 2 x - 1 ,   f 1 = 2