If the area of region bounded by the lines y=2 x+1, x -axis, x=a and x=3 is 10 sq units. Then the value of ' a ' is

Step-by-step solution

The area A of the region bounded by the line y = 2x + 1 , the x -axis, x = a , and x = 3 is given by the definite integral of the function f(x) = 2x + 1 from a to 3 . A = _ a ³ (2x + 1) dx = 10 Evaluating the integral: [x^2 + x]_ a ³ = 10 Substituting the limits: (3^2 + 3) - (a^2 + a) = 10 (9 + 3) - (a^2 + a) = 10 12 - a^2 - a = 10 a^2 + a - 2 = 0 Factoring the quadratic equation: (a + 2)(a - 1) = 0 The possible values for a are a = 1 or a = -2 . Since the region is bounded between x = a and x = 3 , and the line y