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 ________.

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Aicharya · Accepted Answer

d y d x = 2 x + 1 &#8658; &#8747; d y = &#8747; 2 x + 1 d x &#8658; y x = x 2 + 2 x + C Area = 4 8 3 &#8658; 2 &#8747; - 1 - 1 + 1 - C - x + 1 2 - C + 1 d x = 4 8 3 &#8658; 2 - x + 1 3 3 - C x + x - 1 - 1 + 1 - C = 4 8 3 &#8658; - 1 - C 3 + 3 C - 3 C 1 - C - 3 C - 3 + 3 1 - C + 3 = 2 8 &#8658; C = - 1 &#8658; f x = x 2 + 2 x - 1 , &#160; f 1 = 2

Let the curve y = y x be the solution of the differential equation, d y d x = 2 x + 1 . If the numerical…

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