One of the points of intersection of the curves y=1+3 x-2 x^2 and y= 1 x is ( 1 2 , 2 ) . Let the area of the region enclosed by these curves be 1 24 (l 5 + m )- n _ e (1+ 5 ) , where l, ~m , n N . Then l+ m + n is equal to

Step-by-step solution

aligned & A= _ 1 2 ^ 1+ 5 2 (1+3 x-2 x^2- 1 x ) dx & A= [x+ 3 x^2 2 - 2 x^3 3 - x ]_ 1 2 ^ 1+ 5 & A= 1+ 5 2 + 3 2 ( 1+ 5 2 )^2- 2 3 ( 1+ 5 2 )^3- ( 1+ 5 2 ) & - 1 2 - 3 2 ( 1 4 )+ 2 3 ( 1 8 )+ ( 1 2 ) & A= 1 2 + 5 2 + 3 8 + 3 4 5 + 15 8 - 4 3 - 2 3 5 & - 1 2 - 3 8 + 1 12 - (1+ 5 ) & = 5 ( 1 2 + 3 4 - 2 3 )+ 15 8 - 4 3 + 1 12 - (1+ 5 ) & = 14 24 5 + 15 24 - (1+ 5 ) aligned