The line y=m x bisects the area unclosed by lines x=0, y=0 and x= 3 2 and the curve y=1+4 x-x^2 . Then, the value of m is

Step-by-step solution

Given, y=1+4 x-x^2 aligned & d y d x =4-2 x=0 x=2 [point of maxima] & y_ =1+4 2-4=5 aligned when, x=0, y=1 Graph according to question and above information aligned & If y=m x bisects the area bounded & A₁=A₂ & ₀^ 3 / 2 (1+4 x-x^2 ) d x=2 ₀^ 3 / 2 m x d x & [x+2 x^2- x^3 3 ]₀^ 3 / 2 = [m x^2 ]₀^ 3 / 2 & 3 2 +2 9 4 - 27 8 1 3 =m 9 4 & m= 13 6 aligned