If a curve y = a x + b x passes through the point (1,2) and the area bounded by this curve, line x=4 and the X -axis is 8 sq.units, then the value of a-b is

Step-by-step solution

Given the curve y = a x + bx passes through the point (1, 2) , substitution yields: 2 = a + b The area bounded by the curve, line x = 4 , and the X-axis is given by: ₀⁴ (a x + bx) dx = 8 Evaluating the integral: ₀⁴ (a x + bx) dx = [ 2a 3 x^ 3/2 + b 2 x² ]₀⁴ = 16a 3 + 8b Setting this equal to 8 and simplifying: 16a 3 + 8b = 8 2a + 3b = 3 Solving the system a + b = 2 and 2a + 3b = 3 gives a = 3 , b = -1 . The required value is: a - b = 3 - (-1) = 4